It exists 12 factors of 220, a factor of 220 is in arithmetic an integer that we can multiply by another
integer to get 220. Here are the 12 factors of 220: **1; 2; 4; 5; 10; 11; 20; 22; 44; 55; 110; 220.**

Example: 4 is a factor of 220 because 4 multiplied by 55 is equal to 220.

If the product of two whole numbers is equal to 220 then those two whole numbers are factors of 220. So 55 and 4 are both factors of 220.

Remark: The division of 220 by one of its factors gives as quotient another factor of 220 and zero remainder, a factor of 220 is also a divisor of 220.

Example: 20 is a factor of 220, so 220 divided by 20 gives as quotient 11 which is another factor of 220 and the remainder of the division is equal to zero (220/20=11).

Here are all the multiplications of two integers that the product is equal to 220:**1*220=220; 2*110=220; 4*55=220; 5*44=220; 10*22=220; 11*20=220.**

**Here are the prime factors of 220: 2; 5; 11.**

**The prime factorization of 220 is: 2^2*5*11.**

220 is a multiple of 2 then 220 is an even number.

**Factors of 220:**

Justify why 1; 2; 4; 5; 10; 11; 20; 22; 44; 55; 110 and 220 are factors of 220?

Note: A factor of 220 is a whole number that can divide 220 by giving an integer quotient and a remainder that is equal to zero or it's a whole number that we can multiply with another whole number to get 220 as product.

1 is a factor of 220 because 220 divided by 1 is equal to 220 and the remainder of the division is equal to zero.

2 is a factor of 220 because 220 divided by 2 is equal to 110 and the remainder of the division is equal to zero.

4 is a factor of 220 because 220 divided by 4 is equal to 55 and the remainder of the division is equal to zero.

5 is a factor of 220 because 220 divided by 5 is equal to 44 and the remainder of the division is equal to zero.

10 is a factor of 220 because 220 divided by 10 is equal to 22 and the remainder of the division is equal to zero.

11 is a factor of 220 because 220 divided by 11 is equal to 20 and the remainder of the division is equal to zero.

20 is a factor of 220 because the product of the multiplication of 20 by 11 is equal to 220.

22 is a factor of 220 because the product of the multiplication of 22 by 10 is equal to 220.

44 is a factor of 220 because the product of the multiplication of 44 by 5 is equal to 220.

55 is a factor of 220 because the product of the multiplication of 55 by 4 is equal to 220.

110 is a factor of 220 because the product of the multiplication of 110 by 2 is equal to 220.

220 is a factor of 220 because the product of the multiplication of 220 by 1 is equal to 220.

**Multiples of 220:**

Justify if the following whole numbers are multiples of 220: 1980; 1100; 1760; 660; 665; 2420; 2860; 3960; 3740; 3520; 4400; 5060; 5280; 5720; 5727; 7040; 7700; 7920; 8800; 9240.

Note: A positive integer is a multiple of 220 if its division by 220 gives a whole number as quotient and a remainder that is equal to zero.

If a natural number is a multiple of 220 then 220 is its factor.

220 is an even number so all the multiples of 220 are even numbers.

10 is a factor of 220 so the last digit of a multiple of 220 is zero(0).

If we divide 1980 by 220 we get an integer quotient that is equal to 9 and the remainder of the division is equal to zero so 1980 is a multiple of 220 (220 and 9 are factors of 1980).

1100 is divisible by 220 because 1100 divided by 220 gives 5 as quotient and zero remainder.

1920 is the product of the multiplication of 192 and 10 so 1920 is a common multiple of 192 and 10 (192 and 10 are factors of 1920).

By multiplying 220 by 8 we get 1760 as product so 1760 is a multiple of 220 and 8 (220 and 8 are divisors of 1760).

660 is a multiple of 220 and 220 is a factor of 660 because the quotient of the division of 660 by 220 is 3 and the remainder of that division is equal to zero.

2420 divided by 220 gives 11 as quotient and a remainder that is equal to zero so 2420 is a common multiple of 220 and 11 (220 and 11 are factors of 2420).

The multiplication of 220 by 13 gives 2860 as product so 2860 is a commun multiple of 220 and 13 (220 and 13 are divisors of 2860).

220 is a factor of 3960 because the division of 3960 by 220 gives 18 as quotient and a remainder that is equal to zero so 3960 is a multiple of 220.

If we multiply 220 by 17 we get 3740 as product so 3740 is a commun multiple of 220 and 17 (220 and 17 are factors of 3740).

3520 divided by 220 is equal to 16 and the remainder of the division is equal to 0 so 3520 is a multiple of 220 and 220 is a factor of 3520.

4400 is a common multiple of 220 and 20 because the multiplication of 220 and 20 gives 4400 as product so 220 and 20 are factors of 4400.

5060 divided by 220 gives 23 as quotient and the remainder of the division is zero so 5060 is a multiple of 220 and 220 is a factor of 5060.

5280 is divisible by 220 because the division of 5280 by 220 gives 24 as quotient and a remainder that is equal to zero so 5280 is a common multiple of 220 and 24 (220 and 24 are factors of 5280).

By multiplying 220 by 26 we get 5720 as product so 5720 is a multiple of 220 and 26 (220 and 26 are factors of 5720).

5727 is not ended with zero so 5727 is not a multiple of 220 and 220 is not a factor of 5727.

The multiplication of 220 by 32 gives 7040 as product so 7040 is a multiple of 220 and 32 (220 and 32 are factors of 7040).

220 multiplied by 35 gives 7700 as product so 7700 is a multiple of 220 and 35 (220 and 35 are factors of 7700).

7920 divided by 220 is equal to 36 and the remainder of the division is equal to zero so 7920 is a multiple of 220 and 36 (220 and 36 are called divisors or factors of 7920).

The multiplication of 220 by 40 gives 8800 as product so 8800 is a multiple of 220 and 40 (220 and 40 are factors of 8800).

By dividing 9240 by 220 we get 42 as product so 9240 is a multiple of 220 and 42 (220 and 42 are factors of 9240.

**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.

**find the lcm and the gcf of two integers**

**find the first n multiples of an integer**

**find the multiples of an integer inside an interval**

**retrieve prime numbers inside an interval**

**retrieve the irreducible value of a fraction**

Example: 4 is a factor of 220 because 4 multiplied by 55 is equal to 220.

If the product of two whole numbers is equal to 220 then those two whole numbers are factors of 220. So 55 and 4 are both factors of 220.

Remark: The division of 220 by one of its factors gives as quotient another factor of 220 and zero remainder, a factor of 220 is also a divisor of 220.

Example: 20 is a factor of 220, so 220 divided by 20 gives as quotient 11 which is another factor of 220 and the remainder of the division is equal to zero (220/20=11).

Here are all the multiplications of two integers that the product is equal to 220:

220 is a multiple of 2 then 220 is an even number.

Justify why 1; 2; 4; 5; 10; 11; 20; 22; 44; 55; 110 and 220 are factors of 220?

Note: A factor of 220 is a whole number that can divide 220 by giving an integer quotient and a remainder that is equal to zero or it's a whole number that we can multiply with another whole number to get 220 as product.

1 is a factor of 220 because 220 divided by 1 is equal to 220 and the remainder of the division is equal to zero.

2 is a factor of 220 because 220 divided by 2 is equal to 110 and the remainder of the division is equal to zero.

4 is a factor of 220 because 220 divided by 4 is equal to 55 and the remainder of the division is equal to zero.

5 is a factor of 220 because 220 divided by 5 is equal to 44 and the remainder of the division is equal to zero.

10 is a factor of 220 because 220 divided by 10 is equal to 22 and the remainder of the division is equal to zero.

11 is a factor of 220 because 220 divided by 11 is equal to 20 and the remainder of the division is equal to zero.

20 is a factor of 220 because the product of the multiplication of 20 by 11 is equal to 220.

22 is a factor of 220 because the product of the multiplication of 22 by 10 is equal to 220.

44 is a factor of 220 because the product of the multiplication of 44 by 5 is equal to 220.

55 is a factor of 220 because the product of the multiplication of 55 by 4 is equal to 220.

110 is a factor of 220 because the product of the multiplication of 110 by 2 is equal to 220.

220 is a factor of 220 because the product of the multiplication of 220 by 1 is equal to 220.

Justify if the following whole numbers are multiples of 220: 1980; 1100; 1760; 660; 665; 2420; 2860; 3960; 3740; 3520; 4400; 5060; 5280; 5720; 5727; 7040; 7700; 7920; 8800; 9240.

Note: A positive integer is a multiple of 220 if its division by 220 gives a whole number as quotient and a remainder that is equal to zero.

If a natural number is a multiple of 220 then 220 is its factor.

220 is an even number so all the multiples of 220 are even numbers.

10 is a factor of 220 so the last digit of a multiple of 220 is zero(0).

If we divide 1980 by 220 we get an integer quotient that is equal to 9 and the remainder of the division is equal to zero so 1980 is a multiple of 220 (220 and 9 are factors of 1980).

1100 is divisible by 220 because 1100 divided by 220 gives 5 as quotient and zero remainder.

1920 is the product of the multiplication of 192 and 10 so 1920 is a common multiple of 192 and 10 (192 and 10 are factors of 1920).

By multiplying 220 by 8 we get 1760 as product so 1760 is a multiple of 220 and 8 (220 and 8 are divisors of 1760).

660 is a multiple of 220 and 220 is a factor of 660 because the quotient of the division of 660 by 220 is 3 and the remainder of that division is equal to zero.

2420 divided by 220 gives 11 as quotient and a remainder that is equal to zero so 2420 is a common multiple of 220 and 11 (220 and 11 are factors of 2420).

The multiplication of 220 by 13 gives 2860 as product so 2860 is a commun multiple of 220 and 13 (220 and 13 are divisors of 2860).

220 is a factor of 3960 because the division of 3960 by 220 gives 18 as quotient and a remainder that is equal to zero so 3960 is a multiple of 220.

If we multiply 220 by 17 we get 3740 as product so 3740 is a commun multiple of 220 and 17 (220 and 17 are factors of 3740).

3520 divided by 220 is equal to 16 and the remainder of the division is equal to 0 so 3520 is a multiple of 220 and 220 is a factor of 3520.

4400 is a common multiple of 220 and 20 because the multiplication of 220 and 20 gives 4400 as product so 220 and 20 are factors of 4400.

5060 divided by 220 gives 23 as quotient and the remainder of the division is zero so 5060 is a multiple of 220 and 220 is a factor of 5060.

5280 is divisible by 220 because the division of 5280 by 220 gives 24 as quotient and a remainder that is equal to zero so 5280 is a common multiple of 220 and 24 (220 and 24 are factors of 5280).

By multiplying 220 by 26 we get 5720 as product so 5720 is a multiple of 220 and 26 (220 and 26 are factors of 5720).

5727 is not ended with zero so 5727 is not a multiple of 220 and 220 is not a factor of 5727.

The multiplication of 220 by 32 gives 7040 as product so 7040 is a multiple of 220 and 32 (220 and 32 are factors of 7040).

220 multiplied by 35 gives 7700 as product so 7700 is a multiple of 220 and 35 (220 and 35 are factors of 7700).

7920 divided by 220 is equal to 36 and the remainder of the division is equal to zero so 7920 is a multiple of 220 and 36 (220 and 36 are called divisors or factors of 7920).

The multiplication of 220 by 40 gives 8800 as product so 8800 is a multiple of 220 and 40 (220 and 40 are factors of 8800).

By dividing 9240 by 220 we get 42 as product so 9240 is a multiple of 220 and 42 (220 and 42 are factors of 9240.

The first number that is a natural number is 0.