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Divisibility for Fives

Reference > Mathematics > Number Theory > Divisibility Rules
 

The divisibility rule for 5 is even simpler than the divisibility rule for 2. All you need to know is whether the number ends with a 5 or a 0. If it does, it is divisible by 5.

Thus, 15, 245, 360 and 1,000 all are divisible by 5, but 16, 433, and 38 are not.

The divisibility rule for 10 is even simpler: in order to be divisible by 10, a number must end in 0. Of course, there's another way we could say that: it has to be a multiple of 2 and a multiple of 5. To be a multiple of 2, it has to end in 0, 2, 4, 6, or 8, and to be a multiple of 5, it has to end in 0 or 5. Clearly 0 is the only number that fits both those rules!

Divisible by 25? The last two digits have to be divisible by 25. In other words, if it ends in 00, 25, 50, or 75, it's a multiple of 25.

Like the rules for 2, we can generalize this one also: The divisibility rule for 5n is that the last n digits must be divisible by 5n.

And finally, a number is divisible by 10n if it ends in n zeroes.

 

Questions

1.
Is 47 divisible by 5? How do you know?
2.
Is 1,275 divisible by 25? How do you know?
3.
How can you tell if the number 134,254,375 is divisible by 54?
4.
What would be a divisibility rule for 20?
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