Divisibility Test
Test if one number divides another evenly. Free online divisibility test calculator checks divisibility and shows the quotient, remainder, and applicable divisibility rule.
About This Calculator
This divisibility test calculator checks whether a given number is divisible by another number. It performs the division and reports whether the remainder is zero, along with the quotient and remainder values. The calculator also displays the applicable divisibility rule for common divisors (2 through 10), helping students learn and verify these important mathematical shortcuts.
Divisibility rules are quick mental shortcuts that tell you whether one number divides another without performing full division. For example, a number is divisible by 2 if its last digit is even, divisible by 3 if the sum of its digits is divisible by 3, and divisible by 5 if it ends in 0 or 5. This calculator automates these checks and provides a clear yes/no answer.
Educational value: Divisibility rules are taught in elementary and middle school mathematics worldwide. They build foundational number sense, aid in prime factorization, simplify fraction operations, and introduce modular arithmetic concepts. Use this calculator to verify your manual divisibility checks or to explore patterns in number divisibility.
Frequently Asked Questions
What does it mean for a number to be divisible by another?
A number a is divisible by another number b if a ÷ b leaves no remainder. In other words, a is divisible by b when a mod b = 0, meaning the remainder after division is zero.
What is the divisibility rule for 2?
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). For example, 124 is divisible by 2 because it ends in 4, while 125 is not because it ends in 5.
What is the divisibility 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, so 123 is divisible by 3. For 124: 1+2+4=7, and 7 is not divisible by 3, so 124 is not divisible by 3.
What is the divisibility rule for 5?
A number is divisible by 5 if its last digit is 0 or 5. For example, 125 ends in 5 and is divisible by 5, while 124 ends in 4 and is not divisible by 5.
What is the divisibility 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, and 18 is divisible by 9, so 729 is divisible by 9. For 730: 7+3+0=10, and 10 is not divisible by 9.
What is the divisibility rule for 10?
A number is divisible by 10 if its last digit is 0. For example, 120, 340, and 1,000 are all divisible by 10 because they end in 0.
Why are divisibility rules taught in school?
Divisibility rules help students quickly determine whether one number divides another without performing long division. They build number sense, aid in prime factorization, simplify fractions, and are foundational for understanding modular arithmetic and number theory.
What is the divisibility rule for 7?
The divisibility rule for 7 is: double the last digit and subtract it from the rest of the number. Repeat this process until you get a small number. If the result is divisible by 7, the original number is divisible by 7. For example, 161: 16 - 2x1 = 14, which is divisible by 7.