Answer to Question #43871 in Combinatorics | Number Theory for Jakori Price

Question

If a number is a multiple of 64, then it is a multiple of 8.
If a number is a multiple of 8, then it is a multiple of 2.

Answer 1

A multiple is the result of multiplying a number by an integer (not a fraction). Multiplies of 64 are all numbers 64k, where k is integer. Multiplies of 8 are all numbers 8m, where m is integer. Rewrite 64k=8*8k=8m, where m is integer, m=8k. It means the following: if a number is a multiple of 64, then it is a multiple of 8.
Multiplies of 8 are all numbers 8l, where l is integer. Multiplies of 2 are all numbers 2n, where n is integer. Rewrite 8l=2*4l=2n, where n is integer, n=4l. It means the following: if a number is a multiple of 8, then it is a multiple of 2.