Divisibility Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Test

7{,}215

for divisibility by

5

9

, and

10

using divisibility rules.

1
By $5$ : last digit is $5$ . Yes (a number ending in $0$ or $5$ is divisible by $5$ ).
2
By $9$ : digit sum $= 7+2+1+5 = 15$ ; $15 \div 9 = 1.67\ldots$ No.
3
By $10$ : last digit is $5$ , not $0$ . No.

Answer

7{,}215

is divisible by

5

but not by

9

10

Divisibility by

10

requires the last digit to be

0

; divisibility by

5

requires the last digit to be

0

5

. Since

15

is not divisible by

9

, the digit-sum test fails for

9

— a quick check without any division.

About Divisibility Intuition

Understanding when one whole number divides evenly into another, leaving no remainder—the foundation of factor and multiple relationships.

Use divisibility rules to determine whether [formula] is divisible by [formula], [formula], [formula

Explain why the divisibility rule for [formula] works: a number is divisible by [formula] if and onl

A number [formula] leaves remainder [formula] when divided by [formula] and remainder [formula] when