Divisibility Calculator
Divisibility Rules
Understanding Divisibility
Divisibility refers to the ability of one integer to be divided by another integer without leaving a remainder. When we say "a is divisible by b," we mean that a ÷ b results in a whole number.
Divisibility Rules
Divisibility rules are shortcuts that help determine if a number is divisible by another without performing the actual division:
Rule for 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). For example, 246 is divisible by 2 because 6 is even.
Rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 123 → 1+2+3 = 6, and 6 is divisible by 3.
Rule for 4
A number is divisible by 4 if its last two digits form a number that is divisible by 4. For example, 316 → 16 is divisible by 4.
Rule for 5
A number is divisible by 5 if its last digit is 0 or 5. For example, 125 ends in 5, so it is divisible by 5.
Rule for 6
A number is divisible by 6 if it is divisible by both 2 AND 3. For example, 24 is even (divisible by 2) and 2+4=6 is divisible by 3.
Rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9. For example, 729 → 7+2+9 = 18 → 1+8 = 9.
Rule for 10
A number is divisible by 10 if it ends in 0. For example, 150 ends in 0, so it is divisible by 10.
Applications
- Simplifying Fractions: Finding common divisors helps reduce fractions to their simplest form.
- Prime Testing: A number is prime if its only divisors are 1 and itself.
- Cryptography: Divisibility properties are fundamental to many encryption algorithms.
- Computer Science: Used in algorithms, data structures, and hash functions.
Frequently Asked Questions
How do I check if a number is divisible by another?+
Enter the number you want to test and the divisor, then the calculator instantly tells you whether it divides evenly. A number is divisible by another when the division leaves a remainder of zero — for example, 24 is divisible by 6 because 24 ÷ 6 = 4 with no remainder. The tool also shows the quotient and remainder so you can see exactly why a number does or does not divide evenly.
What are the divisibility rules for 2 through 12?+
Divisible by 2 if the last digit is even; by 3 if the digit sum is divisible by 3; by 4 if the last two digits form a multiple of 4; by 5 if it ends in 0 or 5; by 6 if it is divisible by both 2 and 3; by 8 if the last three digits form a multiple of 8; by 9 if the digit sum is divisible by 9; by 10 if it ends in 0; by 11 if the alternating digit sum is a multiple of 11; and by 12 if it is divisible by both 3 and 4. Rules for 7 are more involved, so the calculator tests it directly.
How do I find all the divisors of a number?+
Enter a number and the calculator lists every whole number that divides it evenly, from 1 up to the number itself. This is useful for simplifying fractions, finding common factors, or checking whether a number is prime — a prime number has exactly two divisors, 1 and itself.
Is the divisibility calculator free and does it work on mobile?+
Yes. The tool is completely free, requires no sign-up, and runs entirely in your browser, so nothing is sent to a server. The responsive layout works on phones, tablets, and desktops, making it handy for homework, quick math checks, or teaching divisibility concepts on any device.
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