What does this calculator do?

The divisibility test calculator checks whether an integer is divisible by common divisors without a remainder. This tool, provided by Hesapstan, supports a quick summary mode and a detail mode for learning the rule behind a selected divisor.

• Summary mode checks 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 25.
• Detail mode shows the result, remainder, rule and a short applied explanation for one selected divisor.
• Negative integers are supported; divisibility is evaluated using the absolute value.

Summary mode vs Detail mode

Summary mode checks many common divisors at once, while Detail mode focuses on one divisor and explains the rule used for that case.

• Use Summary mode when you want a quick list of yes/no results.
• Use Detail mode when you want to understand why a number is or is not divisible by a selected divisor.
• The divisor 13 is available in Detail mode only; it is not part of the Summary list.

What does divisibility mean?

A number is divisible by another number when the division leaves a remainder of 0. For example, 15 is divisible by 5 because 15 ÷ 5 = 3 with no remainder.

If the remainder is not 0, the number is not exactly divisible by that divisor. For example, 17 divided by 5 leaves a remainder of 2, so 17 is not divisible by 5.

Which divisibility rules are covered?

The calculator covers only the common divisors supported by its runtime. It should not be read as a complete reference for every possible divisor.

• 2: the last digit is even.
• 3: the digit sum is divisible by 3.
• 4: the last two digits are divisible by 4.
• 5: the last digit is 0 or 5.
• 6: the number is divisible by both 2 and 3.
• 8: the last three digits are divisible by 8.
• 9: the digit sum is divisible by 9.
• 10: the last digit is 0.
• 11: the alternating digit-sum difference is divisible by 11.
• 12: the number is divisible by both 3 and 4.
• 25: the last two digits are 00, 25, 50 or 75.
• For 7 and 13, Detail mode shows the supported rule explanation; this content does not invent a different shortcut rule.

Negative numbers and zero

Negative integers are valid. The calculator evaluates divisibility using the absolute value, so -12 and 12 have the same divisibility pattern for the supported positive divisors.

Examples

These examples are aligned with the calculator behavior.

• For 12, the summary includes divisible by 2, 3, 4, 6 and 12; not divisible by 5, 7, 8, 9, 10, 11 and 25.
• For 100, the summary includes divisible by 2, 4, 5, 10 and 25; not divisible by 3, 6, 7, 8, 9, 11 and 12.
• For -12, the divisibility pattern is the same as 12 because the check uses |n|.
• For 1234 with divisor 9, the digit sum is 1 + 2 + 3 + 4 = 10, so it is not divisible by 9; the remainder is 1.
• For 1001 with divisor 11, the alternating-sum check gives 0, so the number is divisible by 11.
• 3.5 is not a valid input because this tool checks integers only.

How to use the calculator

1. Enter the integer you want to test.
2. Choose Summary mode for a quick list of common divisors.
3. Choose Detail mode and select a divisor when you want the rule explanation.
4. Read the divisibility result, remainder and rule note shown by the calculator.

Divisibility test, modulo and factors

A divisibility test answers whether the remainder is 0. A modulo calculator shows the remainder directly. A factor calculator lists the positive divisors of a number.

Prime factorization and GCD/LCM are related number-theory tools, but they answer different questions from this divisibility test calculator.

Limitations

This calculator is limited to the supported integer divisibility tests. It is not a full modular arithmetic or factorization tool.

• It does not accept decimals, fractions or algebraic expressions.
• 13 appears in Detail mode, not in Summary mode.
• It does not perform prime factorization, factor listing, GCD/LCM or modular arithmetic operations.
• Very large values may be rejected to keep the calculation safe.