Number Divisibility Checker

Check divisibility by any set of divisors — prime factorization, GCD, LCM, and digit sum included.

Number

Divisors to check (comma-separated)

Prime factorization

2^3 × 3^2 × 5

Type

Composite

Digit sum

Divisible by

9/14

Total Number of Divisors (σ₀)

Sum of All Divisors (σ₁)

1170

All Divisors of 360

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Divisor	Divisible?	Remainder
2	Yes	0
3	Yes	0
4	Yes	0
5	Yes	0
6	Yes	0
7	No	3
8	Yes	0
9	Yes	0
10	Yes	0
11	No	8
12	Yes	0
13	No	9
100	No	60
1000	No	360

Divisibility rules and prime factorization

A number is divisible by 2 if its last digit is even; by 3 if its digit sum is divisible by 3; by 5 if it ends in 0 or 5; by 9 if its digit sum is divisible by 9; by 10 if it ends in 0. Prime factorization decomposes a number into its prime building blocks — useful for computing GCDs, LCMs, and solving modular arithmetic problems.

Prime Number Checker GCD & LCM Calculator

Built and maintained by Meet Shah · Last updated 1 August 2026

What this tool is used for

Checking a number against several divisors at once.
Getting a prime factorisation alongside the divisibility results.
Finding a GCD or LCM as part of the same check.
Testing one number against a whole set of divisors in a single pass.
Checking a digit-sum rule against the actual division.

Frequently Asked Questions

What are the quick divisibility rules?: 2 if the last digit is even, 3 if the digit sum is divisible by 3, 4 if the last two digits are, 5 if it ends in 0 or 5, 9 if the digit sum is, and 11 from the alternating digit sum. 7 has no simple rule, which is why it is the one everyone remembers as awkward.
Why does the digit-sum rule work for 3 and 9?: Because 10 ≡ 1 (mod 9), so every power of ten leaves a remainder of 1 and the number is congruent to its digit sum. The same argument gives the alternating sum for 11, since 10 ≡ −1 (mod 11).
Why use BigInt for the factorisation?: Because integers beyond 2⁵³ lose precision as ordinary JavaScript numbers, and a divisibility answer computed on a rounded value is silently wrong. BigInt is exact at any size, which is what makes the result trustworthy for large inputs.
How long can factorisation take?: Trial division is fast for numbers with small factors and slow for a large semiprime, which is exactly the property RSA depends on. A number that is the product of two large primes is the worst case, and the tool bounds the search rather than hanging.
What is the fundamental theorem of arithmetic?: That every integer above 1 has exactly one prime factorisation, up to ordering. It is why factorisation is a canonical description of a number, and why 1 is excluded from the primes — including it would make the factorisation non-unique.

Common errors and gotchas

Applying a digit-sum rule to a divisor it does not work for, since each rule is specific.
Assuming divisibility by two factors implies divisibility by their product, which needs them coprime.
Treating zero as divisible by everything, or dividing by zero, both of which need care.
Expecting factorisation of very large numbers, which trial division cannot do quickly.
Confusing a factor with a divisor's multiple.