Which of the following numbers divides 5,172,324 exactly?

Concept

Divisibility rules test a whole number without performing full long division. For 12, a number must satisfy both the divisibility-by-3 rule and the divisibility-by-4 rule.

A number is divisible by 3 when its digit sum is divisible by 3, and it is divisible by 4 when its last two digits form a multiple of 4.

Application

1. For 5,172,324, the digit sum is 5 + 1 + 7 + 2 + 3 + 2 + 4 = 24. Since 24 is divisible by 3, the number passes the divisibility-by-3 test.

2. Its last two digits are 24. Since 24 is divisible by 4, the number also passes the divisibility-by-4 test.

3. Because both component tests hold, 5,172,324 is divisible by 12.

Cross-check

Direct division gives 5,172,324 ÷ 12 = 431,027, an integer. Therefore, the required divisor is 12.