In the following exercises, use the divisibility tests to determine whether each number is divis

step 1 Okay, so we're going to determine if 75 is divisible by 2, 3, 4, 5, 6, and 10 using common divis

In the following exercises, use the divisibility tests to...

Key Concepts

Divisibility by 6

A number is divisible by 6 if it meets the criteria for both 2 and 3. In other words, a number must be even (divisible by 2) and the sum of its digits must be divisible by 3 for it to be divisible by 6.

Divisibility by 10

A number is divisible by 10 if its last digit is 0. This is because multiples of 10 always end with 0 in the decimal system.

Divisibility by 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This rule is useful because it reduces the problem to a much smaller number when checking large integers.

Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. This is due to the fact that the base-10 system naturally creates this pattern with multiples of 5.

Divisibility by 2

A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). This test is based on the fact that even numbers are multiples of 2.

Divisibility Tests

Divisibility tests are rules or shortcuts that help determine whether one number can be divided evenly by another without needing to perform full division. These tests involve checking specific properties or patterns in a number, such as its last digit or the sum of its digits, in relation to the divisor.

Divisibility by 3

A number is divisible by 3 if the sum of its digits results in a number that is divisible by 3. This rule works regardless of the number of digits because it stems from properties of the base 10 number system.

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