Divisibility Rules - 1-9 Chart - Landscape - Divisibility Rules 1-9 Chart Landscape 1a

Oct 22, 2026

Uploaded by Angel

Divisibility Rules 1-9 provide quick tests for determining whether integers are divisible by 1 through 9 using only their digits and simple arithmetic. The rules cover cases for divisibility by 2, 3, 4, 5, 6, 7, 8, and 9, including step-by-step digit-sum checks and halving tests for the last two or three digits. Worked examples contrast divisible and not-divisible numbers, and special notes clarify whole numbers and the divisibility status of 0.

LanguageEnglish

CategoryExam

FormatPDF

Pages1

Reading Time3 min

AccessFree to download

Divisibility by 1 and Whole Number Notes

Divisibility by 2 and Examples

Divisibility by 3 and Examples

Divisibility by 4 and Examples

Divisibility by 5 and Examples

Divisibility by 6 and Related Rules

Divisibility by 7 and Examples

Divisibility by 8 and Examples

Divisibility by 9 and Examples

Name Date | | | | | --- | --- | --- | | All integers are divisible by 1. | All even numbers are divisible by 2.
This means any integer whose last digit is 0, 2, 4, 6 or 8. | All integers where the total of the digits is divisible by 3 (in the 3 times table) . This rule can be repeated if needed. | | 147 is divisible by 1 because it is a whole number. 2059 is divisible by 1 because it is a whole number.
12.8 is not divisible by 1 because it is not an integer. | 318 is divisible by 2 because the last digit is 8. 8÷2=4 (divisible)
513 is not divisible by 2 because 3÷2=1 ½ (not divisible) . | 714 is divisible by 3 because 7+1+4=12 and 12÷3=4 (divisible) .
3515 is not divisible by 3 because 3+5+1+5=14 . Repeat the rule: 1+4=5 . Not divisible by 3. | | | | | | All even integers whose last two digits are divisible by 4.
A quick way to test this is to halve the last two digits twice and see if you get a whole number. | All integers whose last digit is a 0 or 5. | All even integers which are divisible by 3 (see Divisible by 3 rule) . | | 1328 is divisible by 4 because 28÷4=7 .
793 is not divisible by 4 because it is odd.
870 is not divisible by 4 because half of 70=35 and half of 35=17 ½ (not a whole number) | 4185 is divisible by 5 because the last digit is 5.
319 is not divisible by 5 because the last digit is 9. | 432 is divisible by 3 because it is even and the total of the digits is 4+3+2=9 and 9÷3=3 (divisible) .
158 is not divisible by 3 because 1+5+8=14 and 14÷3=4 2/3 (not divisible) . | | | | | | Double the last digit and subtract the result from the number made by the other digits and see if it is divisible by 7. Repeat again if needed. | All even integers where the last 3 digits are divisible by 8.
A quick way to test this is to halve the last 3 digits three times and see if you get a whole number. | All integers where the total of the digits is divisible by 9 (in the 9 times tables) . This rule can be repeated if needed. | | 1057 is divisible by 7 because 105-2x7=91 . 91÷7=13 (divisible) .
841 is not divisible by 7 because 84–2x1=82 . 82÷7=11 5/7 (not divisible) . | 5312 is divisible by 8 because 312÷8=39 .
1207 is not divisible by 8 because it is odd.
4284 is not divisible by 8 because half of 284=142 and half of 142 is 71 and half of 71 is 35 ½ (not a whole number) | 2745 is divisible by 9 because 2+7+4+5=18 . Yesdivisible by 9.
1024 is not divisible by 9 because 1+0+2+4=7 which is not divisible by 9. | An integer is whole number which can be positive or negative. 0 is divisible by any number except itself.

FAQs

What does it mean for a number to be divisible by 1, and what counts as a whole number?

Any integer is divisible by 1 because it is a whole number. Whole numbers can be positive or negative.

How can you test divisibility by 3 and by 9 using digit sums?

For divisibility by 3, check whether the total of the digits is divisible by 3. For divisibility by 9, check whether the digit sum is divisible by 9.

What is a quick method to test divisibility by 4 or 8?

For 4, use a halving method on the last two digits twice and see if the result is a whole number. For 8, apply a similar halving method on the last three digits three times and verify the final result is a whole number.

Oct 22, 2026

Uploaded by Angel