Divisibility Rules for Numbers 2-10

Study Notes

Divisibility Rules

Divisibility rules, also known as divisibility tests, are shortcuts for determining whether a given number is divisible by a certain divisor without performing a full division. These rules are especially useful for large numbers, as they can save time and make the division process more efficient. In this article, we will discuss the divisibility rules for the numbers 2, 3, 4, 5, 6, 9, and 10.

Divisibility Rule for 2

To test for divisibility by 2, examine the last digit of the number. If the last digit is even (0, 2, 4, 6, or 8), then the number is divisible by 2. For example, 14 is divisible by 2, as its last digit is 4, which is even.

Divisibility Rule for 3

For divisibility by 3, you can use the sum of the digits rule. If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. For example, the number 126 is divisible by 3, as the sum of its digits (1+2+6) is 9, which is a multiple of 3.

Divisibility Rule for 4

To test for divisibility by 4, examine the last two digits of the number. If the last two digits form an even number, then the number is divisible by 4. For example, the number 672 is divisible by 4, as its last two digits (2) form an even number.

Divisibility Rule for 5

For divisibility by 5, you can use the 5-rule. If the last digit of a number is either 0 or 5, then the number is divisible by 5. For example, the number 10 is divisible by 5, as its last digit is 0, which is a multiple of 5.

Divisibility Rule for 6

To test for divisibility by 6, you can use the 2 and 3 rules together. If a number is divisible by both 2 and 3, then it is also divisible by 6. For example, the number 18 is divisible by 6, as it is divisible by 2 (last digit is 8) and 3 (sum of digits is 9).

Divisibility Rule for 9

For divisibility by 9, you can use the sum of digits rule. If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. For example, the number 126 is divisible by 9, as the sum of its digits (1+2+6) is 9, which is a multiple of 9.

Divisibility Rule for 10

To test for divisibility by 10, you can simply examine the last digit of the number. If the last digit is 0, then the number is divisible by 10. For example, the number 10 is divisible by 10, as its last digit is 0.

These divisibility rules can be applied to numbers in any base, not just base 10. They provide a useful shorthand for determining divisibility without performing a full division, making the division process more efficient.

Description

Learn about the divisibility rules for numbers 2, 3, 4, 5, 6, 9, and 10 without performing full divisions. Explore shortcuts like examining the last digits or sum of digits to quickly determine if a number is divisible by a certain divisor.