# Multiples and factors

When “a” divided by “b” is exact, we say that “a” is a multiple of “b”, or “b” is a factor (or divisor) of “a”, or “a” is divisible by “b”.

Example: 3 is a factor (or divisor) of 15 and 15 is a multiple of 3.

We write: Div (15) or

We calculate the multiples of a number by multiplying this number by another number. Example:

We find the factors of a number by doing all the divisions with the lower numbers till the quotient is bigger than the divisor. When the division is exact, the quotient is a divisor too.

Example: 20 : 5 = 4   Then 4 and 5 are factors of 20.
Fact(20) = {1, 20, 2, 10, 4, 5}= Fact(20) = {1, 2, 4, 5, 10, 20}

A number is prime if it has exactly two factors: 1 and itself. If the number is not prime, it is composite.

Example: 20 is composite and 13 is prime.

Exercises:

1.- Calculate the first five multiples of 12 and 13

2.- Calculate all the factors of 28 and 42

3.- Decide if the following numbers are prime or composite numbers: 71, 221 and 233

Solutions:

1.-    12→{12,24,36,48,60}     13→{13,26,39,52,65}

2.- fact(28) = {1,2,4,7,14,28}   fact(42) = {1,2,3,6,7,14,21,42}

3.-  71 and 233 are prime numbers and 221 is composite because 221 = 13·17