Identifying Divisibility by Looking at the Final Digits
You can tell whether a number is divisible by 2, 5, 10, 100, or 1,000 simply by looking at how the number ends — no calculations required.
Divisible by 2
Every even number — that is, every number that ends in 2, 4, 6, 8, or 0 — is divisible by 2. For example, the following bold numbers are divisible by 2:
Divisible by 5
Every number that ends in either 5 or 0 is divisible by 5. The following bold numbers are divisible by 5:
Divisible by 10, 100, or 1,000
Every number that ends in 0 is divisible by 10. The following bold numbers are divisible by 10:
Every number that ends in 00 is divisible by 100:
And every number that ends in 000 is divisible by 1,000:
In general, every number that ends with a string of 0s is divisible by the number you get when you write 1 followed by that many 0s. For example,
900,000 is divisible by 100,000.
235,000,000 is divisible by 1,000,000.
820,000,000,000 is divisible by 10,000,000,000.
When numbers start to get this large, mathematicians usually switch over to scientific notation to write them more efficiently.