Use rules of divisibility to determine whether each number given is divisible by a. 2 b. 3 c. 4

step 1 We want to determine if the number 22 ,335 is divisible by the following numbers, 2, 3, 4, 5, 6,

Use rules of divisibility to determine whether each number...

Key Concepts

Divisibility by 12

A number is divisible by 12 if it is divisible by both 3 and 4. This combined rule leverages the tests for divisibility by 3 (the sum of digits) and 4 (the last two digits) to determine divisibility by 12.

Divisibility by 10

A number is divisible by 10 if its last digit is 0. This rule makes it easy to identify multiples of 10 by looking solely at the final digit.

Divisibility by 9

A number is divisible by 9 if the sum of its digits is a multiple of 9. Like the test for 3, this method condenses the number down to a simple sum to check for divisibility.

Divisibility by 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. This approach works because 1000 is divisible by 8, thus only the last three digits need to be examined.

Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3. This dual condition allows for a combined test using the simpler rules for divisibility by 2 and 3.

Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5. This straightforward rule relies solely on the digit in the ones place.

Divisibility by 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This rule works because 100 is divisible by 4, reducing the test to only the final two digits.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is a multiple of 3. Adding up all the digits of the number and checking this sum simplifies the process of testing for divisibility.

Divisibility by 2

A number is divisible by 2 if its last digit is even. This means that if the digit in the ones place is 0, 2, 4, 6, or 8, the number can be evenly divided by 2.

Divisibility Rules

Divisibility rules are shortcuts that help determine whether one number is divisible by another without performing full division. They use properties such as the last digit(s) or the sum of digits to quickly identify factors of a number.

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