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What are the multiples of 28?
Here are the five first multiples of 28 greater than 0:
28 ; 56 ; 84 ; 112 ; 140
A positive integer is a multiple of 28 when it can be divided by 28; this means that its division by 28 gives
an integer quotient and zero remainder.
Remarks:
Since 28 is a multiple of 2; 4; 7 and 14, all multiples of 28 are also multiples of 2; 4; 7 and 14.
If a natural number is a multiple of 2 and a multiple of 14 then it is also a multiple of 28;
If a natural number is a multiple of 4 and a multiple of 7 then it is also a multiple of 28;
28 is an even number then all multiples of 28 are also even numbers.
In arithmetic if an integer M is a multiple of 28, it exists another natural number P such that we can divide M by 28 to get P; we can
divide M by P to get 28 and we can multiply P by 28 to get M.
Example: 84 divided by 28 is equal to 3 (M=84 and P=3) so the division of 84 by 3 gives 28 and the multiplication
of 3 by 28 gives 84.
28 and 3 are called factors or divisors of 84; 84 is a common multiple of 28 and 3.
In the same way we have also: 28 multiplied by 12 gives 336 and 336 divided by 28 is equal to 12 then 336
is a multiple of 28 and 12.
By multiplying 1 by 28 we find 28; 28 is the first positive integer bigger than zero that is a multiple of 28.
Example: 140 is a multiple of 28 'because 140 is divisible by 2 and 14'.
28 has an infinite number of multiples, here are some positive integers up to 0 that are multiples of 28:
Multiples of 28 less than 1000:
28; 56; 84; 112; 140; 168; 196; 224; 252; 280; 308; 336; 364; 392; 420; 448; 476; 504; 532; 560;
588; 616; 644; 672; 700; 728; 756; 784; 812; 840; 868; 896; 924; 952; 980.
Multiples of 28 up to 1000 and less than 2000:
1008; 1036; 1064; 1092; 1120; 1148; 1176; 1204; 1232; 1260; 1288; 1316; 1344; 1372; 1400; 1428; 1456; 1484; 1512;
1540; 1568; 1596; 1624; 1652; 1680; 1708; 1736; 1764; 1792; 1820; 1848; 1876; 1904; 1932; 1960; 1988.
Multiples of 28 between 2000 and 3000:
2016; 2044; 2072; 2100; 2128; 2156; 2184; 2212; 2240; 2268; 2296; 2324; 2352; 2380; 2408; 2436; 2464; 2492; 2520;
2548; 2576; 2604; 2632; 2660; 2688; 2716; 2744; 2772; 2800; 2828; 2856; 2884; 2912; 2940; 2968; 2996.
Multiples of 28 between 3000 and 4000:
3024 ; 3052 ; 3080 ; 3108 ; 3136 ; 3164 ; 3192 ; 3220 ; 3248 ; 3276 ; 3304 ; 3332 ; 3360 ; 3388 ; 3416 ; 3444 ; 3472 ;
3500 ;
3528 ; 3556 ; 3584 ; 3612 ; 3640 ; 3668 ; 3696 ; 3724 ; 3752 ; 3780 ; 3808 ; 3836 ; 3864 ; 3892 ; 3920 ; 3948 ; 3976
Multiples of 28 between 4000 and 5000:
4004 ; 4032 ; 4060 ; 4088 ; 4116 ; 4144 ; 4172 ; 4200 ; 4228 ; 4256 ; 4284 ; 4312 ; 4340 ; 4368 ; 4396 ; 4424 ; 4452 ;
4480 ; 4508 ;
4536 ; 4564 ; 4592 ; 4620 ; 4648 ; 4676 ; 4704 ; 4732 ; 4760 ; 4788 ; 4816 ; 4844 ; 4872 ; 4900 ; 4928 ; 4956 ; 4984
Multiples of 28 between 5000 and 6000:
5012 ; 5040 ; 5068 ; 5096 ; 5124 ; 5152 ; 5180 ; 5208 ; 5236 ; 5264 ; 5292 ; 5320 ; 5348 ; 5376 ; 5404 ; 5432 ; 5460 ;
5488 ; 5516 ;
5544 ; 5572 ; 5600 ; 5628 ; 5656 ; 5684 ; 5712 ; 5740 ; 5768 ; 5796 ; 5824 ; 5852 ; 5880 ; 5908 ; 5936 ; 5964 ; 5992
The multiples of 28 up to 6000 and less than 8000:
6020 ; 6048 ; 6076 ; 6104 ; 6132 ; 6160 ; 6188 ; 6216 ; 6244 ; 6272 ; 6300 ; 6328 ; 6356 ; 6384 ; 6412 ; 6440 ; 6468 ;
6496 ; 6524 ; 6552 ; 6580 ; 6608 ; 6636 ; 6664 ; 6692 ; 6720 ; 6748 ; 6776 ; 6804 ; 6832 ; 6860 ; 6888 ; 6916 ; 6944 ;
6972 ; 7000 ; 7028 ; 7056 ; 7084 ; 7112 ; 7140 ; 7168 ; 7196 ; 7224 ; 7252 ; 7280 ; 7308 ; 7336 ; 7364 ; 7392 ; 7420 ;
7448 ; 7476 ; 7504 ;
7532 ; 7560 ; 7588 ; 7616 ; 7644 ; 7672 ; 7700 ; 7728 ; 7756 ; 7784 ; 7812 ; 7840 ; 7868 ; 7896 ; 7924 ; 7952 ; 7980 ;
The multiples of 28 greater than 8000 and less than 10000:
8008 ; 8036 ; 8064 ; 8092 ; 8120 ; 8148 ; 8176 ; 8204 ; 8232 ; 8260 ; 8288 ; 8316 ; 8344 ; 8372 ; 8400 ; 8428 ; 8456 ;
8484 ; 8512 ; 8540 ; 8568 ; 8596 ; 8624 ; 8652 ; 8680 ; 8708 ; 8736 ; 8764 ; 8792 ; 8820 ; 8848 ; 8876 ; 8904 ; 8932 ;
8960 ; 8988 ; 9016 ; 9044 ; 9072 ; 9100 ; 9128 ; 9156 ; 9184 ; 9212 ; 9240 ; 9268 ; 9296 ; 9324 ; 9352 ; 9380 ; 9408 ;
9436 ; 9464 ; 9492 ; 9520 ;
9548 ; 9576 ; 9604 ; 9632 ; 9660 ; 9688 ; 9716 ; 9744 ; 9772 ; 9800 ; 9828 ; 9856 ; 9884 ; 9912 ; 9940 ; 9968 ; 9996
The multiples of 28 greater than 10000 and less than 12000:
10024 ; 10052 ; 10080 ; 10108 ; 10136 ; 10164 ; 10192 ; 10220 ; 10248 ; 10276 ; 10304 ; 10332 ; 10360 ; 10388 ; 10416 ;
10444 ; 10472 ; 10500 ; 10528 ; 10556 ; 10584 ; 10612 ; 10640 ; 10668 ; 10696 ; 10724 ; 10752 ; 10780 ; 10808 ; 10836 ;
10864 ; 10892 ; 10920 ; 10948 ; 10976 ; 11004 ; 11032 ; 11060 ; 11088 ; 11116 ; 11144 ; 11172 ; 11200 ; 11228 ; 11256 ;
11284 ; 11312 ; 11340 ; 11368 ; 11396 ; 11424 ; 11452 ; 11480 ; 11508 ; 11536 ; 11564 ;
11592 ; 11620 ; 11648 ; 11676 ; 11704 ; 11732 ; 11760 ; 11788 ; 11816 ; 11844 ; 11872 ; 11900 ; 11928 ; 11956 ; 11984
The multiples of 28 greater than 12000 and less than 14000:
12012 ; 12040 ; 12068 ; 12096 ; 12124 ; 12152 ; 12180 ; 12208 ; 12236 ; 12264 ; 12292 ; 12320 ; 12348 ; 12376 ; 12404 ;
12432 ; 12460 ; 12488 ; 12516 ; 12544 ; 12572 ; 12600 ; 12628 ; 12656 ; 12684 ; 12712 ; 12740 ; 12768 ; 12796 ; 12824 ;
12852 ; 12880 ; 12908 ; 12936 ; 12964 ; 12992 ; 13020 ; 13048 ; 13076 ; 13104 ; 13132 ; 13160 ; 13188 ; 13216 ; 13244 ;
13272 ; 13300 ; 13328 ; 13356 ; 13384 ; 13412 ; 13440 ; 13468 ; 13496 ; 13524 ; 13552 ;
13580 ; 13608 ; 13636 ; 13664 ; 13692 ; 13720 ; 13748 ; 13776 ; 13804 ; 13832 ; 13860 ; 13888 ; 13916 ; 13944 ; 13972
The multiples of 28 between 14000 and 16000:
14000 ; 14028 ; 14056 ; 14084 ; 14112 ; 14140 ; 14168 ; 14196 ; 14224 ; 14252 ; 14280 ; 14308 ; 14336 ; 14364 ; 14392 ;
14420 ; 14448 ; 14476 ; 14504 ; 14532 ; 14560 ; 14588 ; 14616 ; 14644 ; 14672 ; 14700 ; 14728 ; 14756 ; 14784 ; 14812 ;
14840 ; 14868 ; 14896 ; 14924 ; 14952 ; 14980 ; 15008 ; 15036 ; 15064 ; 15092 ; 15120 ; 15148 ; 15176 ; 15204 ; 15232 ;
15260 ; 15288 ; 15316 ; 15344 ; 15372 ; 15400 ; 15428 ; 15456 ; 15484 ; 15512 ; 15540 ; 15568 ; 15596 ;
15624 ; 15652 ; 15680 ; 15708 ; 15736 ; 15764 ; 15792 ; 15820 ; 15848 ; 15876 ; 15904 ; 15932 ; 15960 ; 15988 ;
The multiples of 28 greater than 16000 and less than 18000:
16016 ; 16044 ; 16072 ; 16100 ; 16128 ; 16156 ; 16184 ; 16212 ; 16240 ; 16268 ; 16296 ; 16324 ; 16352 ; 16380 ; 16408 ;
16436 ; 16464 ; 16492 ; 16520 ; 16548 ; 16576 ; 16604 ; 16632 ; 16660 ; 16688 ; 16716 ; 16744 ; 16772 ; 16800 ; 16828 ;
16856 ; 16884 ; 16912 ; 16940 ; 16968 ; 16996 ; 17024 ; 17052 ; 17080 ; 17108 ; 17136 ; 17164 ; 17192 ; 17220 ; 17248 ;
17276 ; 17304 ; 17332 ; 17360 ; 17388 ; 17416 ; 17444 ; 17472 ; 17500 ; 17528 ; 17556 ;
17584 ; 17612 ; 17640 ; 17668 ; 17696 ; 17724 ; 17752 ; 17780 ; 17808 ; 17836 ; 17864 ; 17892 ; 17920 ; 17948 ; 17976
Exercise:
Justify if the following integers are multiples of 28:
56; 80; 140; 79; 280; 115; 84; 98; 168; 170; 173; 252; 257; 308; 315; 364; 377; 420; 423; 532; 540; 700; 728; 730; 840.
Correction:
All the multiples of 28 are even numbers because 28 is an even number, so if an integer is an odd number it can't be
a multiple of 28.
56 divided by 28 gives a quotient equal to 2 and the remainder of the division is zero so 56 is a multiple of 28;
80 divided by 28 gives a quotient equal to 2 and the remainder of the division is 24 so 80 is not a multiple of 28;
The multiplication of 28 and 5 gives 140 as product then 140 is a multiple of 28;
The division of 79 by 28 gives 2 as quotient and the remainder of the division is equal to 23 so 79 is not a multiple of 28 and
79 is an odd number it cannot be a multiple of an even number like 28;
280 is a multiple of 28 because 280 is the product of the multiplication of 28 and 10;
115 is not a multiple of 28 because 115 is an odd number;
By dividing 84 by 28 we find 3 as quotient and the remainder of the division is equal to zero so 84 is a multiple of 28;
28 divides 98 by giving a quotient equal to 3 and a remainder equal to 14 so 98 is not a multiple of 28;
168 is divisible by 28, the division of 168 by 28 gives 6 as quotient and zero remainder so 168 is a multiple of 28;
170 divided by 28 gives 6 as quotient and the remainder of the division is equal to zero so 170 is not a multiple of 28;
173 is an odd number so 173 is not a multiple of 28;
28 multiplied by 9 is equal to 252 so 252 is a multiple of 28;
257 is an odd number so 257 is not a multiple of 28;
308 is divisible by 28, the division of 308 by 28 gives 11 as quotient and zero remainder so 308 is a multiple of 28;
315 is an odd number so 315 is not a multiple of 28;
If we multiply 28 by 13 we find 364 so 364 is a multiple of 28;
377 is an odd number so 377 is not a multiple of 28;
If we divide 420 by 28 we find 15 as quotient and the remainder of the division is equal two zero so 420 is a multiple of 28;
423 is an odd number so 423 is not a multiple of 28;
By multiplying 28 by 19 we find 532 so 532 is a multiple of 28;
If we divide 540 by 28 we find 19 as quotient and the remainder of the division is equal to 8 so 540 is not a multiple of 28;
The multiplication of 28 by 25 gives 700 as product so 700 is a multiple of 28;
28 multiplied by 26 gives 728 as product so 728 is a multiple of 28 and 28 is a divisor and factor of 728;
730 divided by 28 gives 26 as quotient and the remainder of the division is equal to 2 so 730 is not a multiple of 2;
28 multiplied by 30 gives 840 as product so 840 is a multiple of 28 and 28 is a divisor and factor of 840;
Is 28 a multiple of 7?
Yes 28 is a multiple of 7, because 28/7 = 4 and 7*4 = 28.
Set of numbers
The set of natural integers is denoted N, the natural integers are numbers which are written
without sign (positive or negative) and without commas. There are an infinite number of natural whole numbers, all
natural numbers are written from the combination of the 10 digits that exist (0; 1; 2; 3; 4; 5; 6; 7; 8; 9).
Note: A digit is also a whole number, whole numbers range from 0 to plus infinity.
Among the natural integers there are even numbers and odd numbers, even numbers are
numbers divisible by 2 while odd numbers are not divisible by 2
(Example: 3 is an odd number and 4 is an even number).
Among the natural integers there are also prime numbers, a prime number is an integer
which has only two divisors the number 1 and the prime number itself
(ex: 11 is a prime number because 11 only has two divisors: 1 and 11).
The set of natural integers is included in the set of relative integers. The
relatives integers are integers that are written with a plus (+) or minus (-) sign. All whole
numbers are positive relative integers because their sign is (+) when the sign of an relative integer
is positive we can not write the sign (+). Example: 4; -5; +12; -70 are relative integers.
The set of relative integers is denoted Z.
The set of relative integers is included in the set of relative decimal numbers, a relative decimal number
is a number that is written with a positive (+) or negative (-) sign and which can also be written with or without
point. Ex: 12; -18; +34; -45.8; +23.5 are relative decimal numbers.
The set of relative decimal numbers is denoted D.
The set of relative decimal numbers is included in the set of rational numbers, the rational numbers are
numbers that are written as fractions, a rational number is therefore a fraction whose numerator
is a relative integer and the denominator is a non-zero (different from zero) natural integer.
Example: 2/3; 12/19; -5/7 are rational numbers.
The set of rational numbers is denoted Q and is included in the set of real numbers.
A real number is made up of rational numbers and irrational numbers.
An irrational number is a number that cannot be written as a fraction whose numerator
is a relative integer and the denominator is a non-zero natural number. Most irrational numbers are
square roots of natural integers.
The set of rational numbers and irrational numbers constitute the set of real numbers denoted R.
We therefore have: N includes in Z includes in D includes in Q includes in R.
Arithmetic and algebra expressions:
Positive integer: Positive integers or natural numbers are numbers that are written only by using the combination of the ten existing
digits (0; 1; 2; 3; 4; 5; 6; 7; 8; 9). The natural numbers are infinite, we cannot list them all.
The first number that is a natural number is 0.
Rational number: Rational numbers are numbers we can write them as fractions that the numerators are
relative integers and the denominators are whole numbers different from zero.
Fraction: A fraction is a division where the dividend is called the numerator and the divisor is called the denominator.
Factors : A factor of a whole number is a positive integer that can divide that whole number, each whole number
has at least two factors.
Common factors: If a natural number divides two numbers by giving an integer quotient and zero remainder then that
natural number is a common factor or common divisor of the two numbers.
Prime factors: A prime factor of a whole number is its factor that is a prime number.
Composite numbers: a composite number is a natural number that is not a prime number.
Even numbers: An even number is a positive integer that is divisible by 2.
Odd numbers: An odd number is a positive integer that is not divisible by 2.
Decimals : decimals are all numbers that can be written with a point or not, all natural number are decimals but
all decimal numbers are not natural numbers.
Substraction : a subtraction is one of the four arithmetic operations that allows you to tell the difference between two numbers.
Divisibility rules : a rule of divisibility helps to know if a natural number is divisible by another
natural number or not.