Type a whole number to see it broken down into prime numbers multiplied together. You get the factors in a row and in power form, a factor tree, the step-by-step division, and how many divisors the number has. Below is a ready table of prime factorisations for every number from 2 to 1000.
Type a whole number of 2 or more.
Read the prime factors and the power form.
Follow the factor tree or the division steps.
Scroll to the table for numbers up to 1000.
Method: Divide by 2 while you can, then 3, then 5, then 7 … until 1 is left
Power form: N = p₁^a × p₂^b × p₃^c …
Number of divisors: (a + 1) × (b + 1) × (c + 1) …
Prime factorisation means writing a whole number as a product of prime numbers only. A prime number, such as 2, 3, 5, 7 or 11, cannot be divided evenly by anything except 1 and itself. Every other number can be split into primes: 100 becomes 2 × 2 × 5 × 5. The prime factorisation calculator does this splitting for any whole number up to very large values.
It gives the answer in three forms so that it matches whatever your textbook asks for: the factors written out in a row, the short power form such as 2² × 5², and a factor tree drawn branch by branch. It also shows the division method line by line and tells you how many divisors the number has. A table underneath lists the prime factorisation of every number from 2 to 1000, handy for checking homework quickly.
1. Start with the smallest prime, 2. If the number divides by 2 exactly, divide and write 2 down.
2. Keep dividing by 2 until it no longer goes in exactly.
3. Move to the next prime, 3, and do the same. Then 5, 7, 11 and so on.
4. Stop when the number left is 1, or when what is left is itself a prime.
5. Write all the primes you used, multiplied together.
6. Group repeated primes as powers, for example 2 × 2 × 2 = 2³.
Just as every word is made from letters, every whole number greater than 1 is made by multiplying primes. What makes this useful is that the set of primes for a number is always the same, no matter how you start splitting. You may break 60 into 6 × 10 or into 4 × 15, but the ends of the branches will always be two 2s, one 3 and one 5. Mathematicians call this the fundamental theorem of arithmetic.
When checking whether a number can be divided, you need to try primes only up to its square root. If a number had a factor bigger than its square root, the matching partner factor would be smaller than the square root, and you would have found that one already. So for 97 you try only 2, 3, 5 and 7. None of them divides it, which proves that 97 is prime.
Once a number is in power form, many questions become easy. The number of divisors is found by adding 1 to each power and multiplying, so 100 = 2² × 5² has 3 × 3 = 9 divisors. A number is a perfect square exactly when every power is even. The HCF of two numbers takes each shared prime with its smaller power, and the LCM takes every prime with its larger power.
For a Class 6 exercise, Meena has to write 360 as a product of primes and say how many factors it has.
Divide by the smallest prime that goes in, again and again: 360 ÷ 2 = 180 180 ÷ 2 = 90 90 ÷ 2 = 45 45 ÷ 3 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1
Stop when you reach 1. The divisors are the prime factors: 360 = 2 × 2 × 2 × 3 × 3 × 5
Write repeated factors as powers: 360 = 2^3 × 3^2 × 5
Number of factors (divisors): Add 1 to each power and multiply: (3 + 1) × (2 + 1) × (1 + 1) = 24
Answer: Prime factorisation 360 = 2 × 2 × 2 × 3 × 3 × 5; Different prime factors 2, 3, 5; Total prime factors 6
Stopping too early with a factor that is not prime, such as writing 100 = 4 × 25.
Counting 1 as a prime factor. 1 is not a prime.
Forgetting a repeated factor, for example writing 12 = 2 × 3 instead of 2 × 2 × 3.
Trying to divide by numbers that are not prime, like 4 or 6, which wastes time.
Mixing up factors and prime factors. The factors of 12 are 1, 2, 3, 4, 6 and 12; its prime factors are only 2 and 3.
Finding the HCF and LCM of two or more numbers.
Reducing fractions to their lowest terms.
Simplifying square roots and cube roots.
Checking whether a number is a perfect square or cube.
Number-system questions in school and competitive exams.
What is the prime factorisation of 100?
100 = 2 × 2 × 5 × 5, or 2² × 5² in power form.
Is 1 a prime number?
No. A prime has exactly two different factors. 1 has only one, so it is neither prime nor composite.
Can a number have two different prime factorisations?
No. Apart from the order of the factors, every number has exactly one. This is called the fundamental theorem of arithmetic.
How do I draw a factor tree?
Split the number into any two factors, then split each of those again, and stop a branch when it reaches a prime. The primes at the ends of the branches are the answer.
How does this help with HCF and LCM?
Write both numbers in prime factors. The HCF uses the primes they share with the lowest powers, and the LCM uses every prime with its highest power.