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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:

image0.jpg

Divisible by 5

Every number that ends in either 5 or 0 is divisible by 5. The following bold numbers are divisible by 5:

image1.jpg

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:

image2.jpg

Every number that ends in 00 is divisible by 100:

image3.jpg

And every number that ends in 000 is divisible by 1,000:

image4.jpg

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.

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