# Synthesis of Multiples & Divisibility

SYNTHESIS OF MULTIPLES AND DIVISIBILITY

Refer back to the multiples work and the charts constructed to find the multiples of numbers up to 10 (circling the numbers in different colors). Repeat this work making new observations-i.e. A number is a multiple of (is divisible by) 6 if it is also a multiple of 2 and 3. This is noticed when the charts for 2, 3, and 6 are done simultaneously. A multiple of 6 intersects the lines of multiples of 2 and 3.
This work really shows the close relationship of multiples and divisibility. Knowledge of one reinforces the other.

Take Table C with the prime factors. Here also we can find, for example, by what numbers 18 is divisible, by making all possible combinations of the prime factors:
18 = 2 x 3 x 3.
18 is divisible by 2, 3, 6, and 9.
18 is even, thus it is divisible by 2.
1 + 8 = 9, thus 18 is divisible by 9, which means it is also divisible by 3.
Since 18 is divisible by 2 and 3, it is also divisible by 6.