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## What are the multiples of 29?

The first 20 multiples of 29 greater than 0 are: 29 ; 58 ; 87 ; 116 ; 145 ; 174 ; 203 ; 232 ; 261 ; 290 ; 319 ; 348 ; 377 ; 406 ; 435 ; 464 ; 493 ; 522 ; 551 ; 580.
If a positive integer is a multiple of 29 we can divide it by 29 to find an integer quotient and zero remainder. We can also multiply 29 by another positive integer to get it (the multiple of 29).
If a whole number is a multiple of 29 we say it is divisible by 29 or 29 divides the whole number (29 is its divisor or its factor).
Example: Let's verify if 87 is a multiple of 29.
By dividing 87 by 29 we get 3 as integer quotient and the remainder of the division is equal to zero. 29 multiplied by 3 gives 87. Those two arithmetic operations (the multiplication and the division) show that 87 is a multiple of 29 because 87 divided by 29 gives an integer quotient and zero remainder, and the product of 29 and 3 is equal to 87.
Remark:
29 is a prime number, if the decomposition into product of prime factors of an integer contains 29 then that integer is a multiple of 29.
Since 29 is an odd number its multiples are positive integers that are odd numbers or even numbers. All positive integers have an infinite number of multiples, so does 29.
Here are some multiples of 29 greater than 0:
Multiples of 29 less than 1000:
29; 58; 87; 116; 145; 174; 203; 232; 261; 290; 319; 348; 377; 406; 435; 464; 493; 522; 551; 580; 609; 638; 667; 696; 725; 754; 783; 812; 841; 870; 899; 928; 957; 986.

Multiples of 29 up to 1000 and less than 2000:
1015; 1044; 1073; 1102; 1131; 1160; 1189; 1218; 1247; 1276; 1305; 1334; 1363; 1392; 1421; 1450; 1479; 1508; 1537; 1566; 1595; 1624; 1653; 1682; 1711; 1740; 1769; 1798; 1827; 1856; 1885; 1914; 1943; 1972.

Multiples of 29 between 2000 and 3000:
2001; 2030; 2059; 2088; 2117; 2146; 2175; 2204; 2233; 2262; 2291; 2320; 2349; 2378; 2407; 2436; 2465; 2494; 2523; 2552; 2581; 2610; 2639; 2668; 2697; 2726; 2755; 2784; 2813; 2842; 2871; 2900; 2929; 2958; 2987.

Multiples of 29 up to 4000 and less than 5000:
4002; 4031; 4060; 4089; 4118; 4147; 4176; 4205; 4234; 4263; 4292; 4321; 4350; 4379; 4408; 4437; 4466; 4495; 4524; 4553; 4582; 4611; 4640; 4669; 4698; 4727; 4756; 4785; 4814; 4843; 4872; 4901; 4930; 4959; 4988.

Multiples of 29 up to 5000 and less than 8000:
5017 ; 5046 ; 5075 ; 5104 ; 5133 ; 5162 ; 5191 ; 5220 ; 5249 ; 5278 ; 5307 ; 5336 ; 5365 ; 5394 ; 5423 ; 5452 ; 5481 ; 5510 ; 5539 ; 5568 ; 5597 ; 5626 ; 5655 ; 5684 ; 5713 ; 5742 ; 5771 ; 5800 ; 5829 ; 5858 ; 5887 ; 5916 ; 5945 ; 5974 ; 6003 ; 6032 ; 6061 ; 6090 ; 6119 ; 6148 ; 6177 ; 6206 ; 6235 ; 6264 ; 6293 ; 6322 ; 6351 ; 6380 ; 6409 ; 6438 ; 6467 ; 6496 ; 6525 ; 6554 ; 6583 ; 6612 ; 6641 ; 6670 ; 6699 ; 6728 ; 6757 ; 6786 ; 6815 ; 6844 ; 6873 ; 6902 ; 6931 ; 6960 ; 6989 ; 7018 ; 7047 ; 7076 ; 7105 ; 7134 ; 7163 ; 7192 ; 7221 ; 7250 ; 7279 ; 7308 ; 7337 ; 7366 ; 7395 ; 7424 ; 7453 ; 7482 ; 7511 ; 7540 ; 7569 ; 7598 ; 7627 ; 7656 ; 7685 ; 7714 ; 7743 ; 7772 ; 7801 ; 7830 ; 7859 ; 7888 ; 7917 ; 7946 ; 7975

Multiples of 29 up to 8000 and less than 10000:
8004 ; 8033 ; 8062 ; 8091 ; 8120 ; 8149 ; 8178 ; 8207 ; 8236 ; 8265 ; 8294 ; 8323 ; 8352 ; 8381 ; 8410 ; 8439 ; 8468 ; 8497 ; 8526 ; 8555 ; 8584 ; 8613 ; 8642 ; 8671 ; 8700 ; 8729 ; 8758 ; 8787 ; 8816 ; 8845 ; 8874 ; 8903 ; 8932 ; 8961 ; 8990 ; 9019 ; 9048 ; 9077 ; 9106 ; 9135 ; 9164 ; 9193 ; 9222 ; 9251 ; 9280 ; 9309 ; 9338 ; 9367 ; 9396 ; 9425 ; 9454 ; 9483 ; 9512 ; 9541 ; 9570 ; 9599 ; 9628 ; 9657 ; 9686 ; 9715 ; 9744 ; 9773 ; 9802 ; 9831 ; 9860 ; 9889 ; 9918 ; 9947 ; 9976

Multiples of 29 up to 10000 and less than 12000:
10005 ; 10034 ; 10063 ; 10092 ; 10121 ; 10150 ; 10179 ; 10208 ; 10237 ; 10266 ; 10295 ; 10324 ; 10353 ; 10382 ; 10411 ; 10440 ; 10469 ; 10498 ; 10527 ; 10556 ; 10585 ; 10614 ; 10643 ; 10672 ; 10701 ; 10730 ; 10759 ; 10788 ; 10817 ; 10846 ; 10875 ; 10904 ; 10933 ; 10962 ; 10991 ; 11020 ; 11049 ; 11078 ; 11107 ; 11136 ; 11165 ; 11194 ; 11223 ; 11252 ; 11281 ; 11310 ; 11339 ; 11368 ; 11397 ; 11426 ; 11455 ; 11484 ; 11513 ; 11542 ; 11571 ; 11600 ; 11629 ; 11658 ; 11687 ; 11716 ; 11745 ; 11774 ; 11803 ; 11832 ; 11861 ; 11890 ; 11919 ; 11948 ; 11977

Exercise:
Justify if the following natural numbers are multiples of 29: 145; 348; 290; 116; 350; 435; 100; 580; 585; 1189; 1190; 1508; 1510; 1595; 1914; 957; 203; 575; 1102; 213; 812; 609.
Correction:
Note: 29 is an odd number and a prime number, the multiples of 29 are odd numbers and even numbers.
145 is a multiple of 29 the division of 145 by 29 gives 5 as quotient and the remainder of that division is equal to zero.
29 divides 348 by giving 12 as quotient and zero (0) as remainder so 348 is a common multiple of 29 and 12 (29 and 12 are divisors of 348).
The multiplication of 29 by 10 is equal to 290 so 290 is a common multiple of 29 and 10.
By multiplying 29 by 4 we get 116 as product so 116 is a common multiple of 29 and 16 (29 and 16 are factors of 116).
350 is not divisible by 29 because the division of 350 by 29 gives 12 as quotient and the remainder of the division is equal to 2 so 350 is not a multiple of 29.
By dividing 435 by 29 we find 15 as quotient and the remainder of the division is equal to zero so 435 is a multiple of 29.
100 is not a multiple of 29 because 29 divides 100 by giving 3 as quotient and the remainder of the division of 100 by 29 is different from zero.
580 divided by 29 gives 20 as quotient and the remainder of the division is equal to zero so 580 is a common multiple of 29 and 20 (29 and 20 are factors or divisors of 580).
We cannot find a natural number to multiply 29 and get 585 as product so 585 is not a multiple of 29.
29 multiplied by 41 gives 1189 as product so 1189 is a common multiple of 29 and 41.
1190 divided by 29 gives 41 as quotient and a remainder that is equal to 1 so 1190 is not a multiple of 29.
1508 is a multiple of 29 because the multiplication of 29 by 52 is equal to 1508.
The division of 1510 by 29 gives 52 as quotient and the remainder of the division is not null (remainder=2) so 1510 is not a multiple of 29.
1595 is divisible by 29 because 29 multiplied by 55 is equal to 1595 so 1595 is a multiple of 29.
1914 divided by 29 is equal to 66 and the remainder of the division is equal to zero so 1914 is a multiple of 29.
If we divide 957 by 29 we find 33 as quotient and the remainder of the division is equal two zero so 957 is a multiple of 29.
If we multiply 29 by 7 we get 203 as product so 203 is a multiple of 29.
By multiplying 29 with 25 we find 575 as product so 575 is a multiple of 29.
If we divide 1102 by 29 we find 38 as quotient and the remainder of the division is equal to zero so 1102 is a multiple of 29.
The remainder of the division of 213 by 29 is different from zero so 213 is not a multiple of 29.
The multiplication of 29 by 28 gives 812 as product so 812 is a common multiple of 29 and 28.
The multiplication of 29 by 21 gives 609 as product so 609 is a common multiple of 29 and 21.

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.

Is 29 a multiple of 3?
29 is not a multiple of 3 because 29 is a prime number and has only two divisors: 1 and 29. Since 3 is not a divisor of 29 then 29 is not a multiple of 3.