Prime Factorisation
Numbers & arithmetic
Factor tree + prime power form for any integer ≤ 10⁹.
Number
Factorisation
Factor tree
- 360
- 2(prime)
- 180
- 2(prime)
- 90
- 2(prime)
- 45
- 3(prime)
- 15
- 3(prime)
- 5(prime)
Frequently asked questions
▶What is prime factorisation?
It breaks a number into a product of prime numbers. For 60, the prime factorisation is 2 times 2 times 3 times 5, often written as 2 squared times 3 times 5. The tool shows both the expanded form and the exponent form, so you can pick whichever your teacher prefers.
▶How do I use this prime factorisation calculator?
Type any whole number from 2 upwards and the prime factors appear instantly. For example, enter 360 and you get 2 cubed times 3 squared times 5. It also lists all the divisors of the number, which is useful for finding factors quickly in word problems.
▶What is the prime factorisation of 1?
1 has no prime factorisation, because 1 is not a prime number. Primes are numbers greater than 1 that have exactly two divisors. The tool returns a clear message for 1 instead of empty output. For 0 it also explains that 0 cannot be factorised in the usual sense.
▶Why are primes important in everyday life and in India?
Primes are the building blocks of all whole numbers and they sit behind UPI security, bank OTPs and WhatsApp encryption. Every secure transaction in India relies on the difficulty of factorising very large numbers. So even small examples like 21 equals 3 times 7 hint at the maths that protects your money.
▶Prime factorisation versus divisors: what is the difference?
Prime factorisation lists only the prime building blocks of a number. Divisors are all numbers that divide it, prime or not. For 12, the prime factorisation is 2 squared times 3, while the divisors are 1, 2, 3, 4, 6 and 12. The tool shows both so you can compare them side by side.
▶Can it factorise very large numbers like 9,99,999?
Yes, up to numbers with around 12 to 14 digits, the tool is quick. For 9,99,999 it returns 3 cubed times 3 times 7 times 11 times 13 times 37, all within a fraction of a second. For cryptography-sized numbers with hundreds of digits, no browser tool can factorise : that is the whole basis of modern encryption.