Balanced factor tree
The tree splits each number into the two factors closest to its square root, so even large numbers give a neat, readable diagram.
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Prime Factorization Calculator Factor Tree, All Factors & Step-by-Step Division
Type any whole number to see its prime factors in exponent form, a visual factor tree and the division ladder you would write by hand. This free prime factorization calculator also lists every factor and factor pair and tells you whether the number is prime.
- Visual factor tree
- Numbers up to 9 quadrillion
- Steps for homework
Prime factorization calculator
Try:
Prime factorizationComposite
360 = 23 × 32 × 5
2 × 2 × 2 × 3 × 3 × 5
- Number of factors
- 24
- Sum of factors
- 1,170
- Distinct primes
- 3
- Euler's totient φ
- 96
- Number type
- Abundant
- Square or cube
- Neither
- Previous prime
- 359
- Next prime
- 367
Features
More than a list of prime factors
Most calculators stop at the answer. This one also shows the working and the number facts teachers and puzzle fans actually ask about.
Division ladder steps
See the repeated division method exactly as it is taught in class, dividing by the smallest prime each time until you reach 1.
Every factor and pair
Get the full sorted list of factors with the primes highlighted, plus every factor pair that multiplies to your number.
Instant prime check
Know at a glance whether a number is prime or composite, along with the nearest primes on either side of it.
Useful number facts
Number of factors, sum of factors, Euler's totient, perfect, abundant or deficient, and whether it is a perfect square or cube.
Huge numbers, fast
Factor any whole number up to 9,007,199,254,740,991 in your browser, usually in well under a second, with nothing uploaded.
How to use
How to use the prime factorization calculator
Enter a number
Type any whole number from 1 upwards. Commas and spaces are ignored, so 1,000,000 works fine.
Read the factorization
Results update as you type. The top card shows the exponent form and the expanded product.
Explore the working
Switch between the factor tree, division steps, all factors and factor pairs using the tabs.
Copy or share
Copy the result for your notes, or copy a link that opens the calculator with your number.
Learn
How to find the prime factorization of a number
There are two classic methods. Both always lead to the same primes, because every whole number above 1 has exactly one prime factorization.
Method 1: the factor tree
Write the number at the top and split it into any two factors. Keep splitting every composite branch until each one ends in a prime, then multiply the primes together.
360 → 18 × 20 → …Method 2: repeated division
Divide by the smallest prime that goes in evenly, starting with 2. Repeat with each answer, moving to 3, 5, 7 and so on, until you reach 1.
360 ÷ 2 = 180 … 5 ÷ 5 = 1Write it in exponent form
Group repeated primes with powers. Three 2s become 23 and two 3s become 32, which is shorter and easier to compare.
2·2·2·3·3·5 = 23·32·5Count the factors
Add 1 to each exponent and multiply the results. This gives the total number of factors without listing them all.
(3+1)(2+1)(1+1) = 24Quick divisibility tests
Even numbers divide by 2. If the digit sum divides by 3, so does the number. Numbers ending in 0 or 5 divide by 5.
360: even, 3+6+0 = 9, ends in 0When to stop
You only need to test primes up to the square root. If none divides the number, what is left is itself prime.
√97 ≈ 9.8, so 97 is primeReference
Prime factorization of numbers 2 to 100
A quick reference chart. Primes are shown in green; for anything bigger, use the calculator above.
- 2
- prime
- 3
- prime
- 4
- 22
- 5
- prime
- 6
- 2 × 3
- 7
- prime
- 8
- 23
- 9
- 32
- 10
- 2 × 5
- 11
- prime
- 12
- 22 × 3
- 13
- prime
- 14
- 2 × 7
- 15
- 3 × 5
- 16
- 24
- 17
- prime
- 18
- 2 × 32
- 19
- prime
- 20
- 22 × 5
- 21
- 3 × 7
- 22
- 2 × 11
- 23
- prime
- 24
- 23 × 3
- 25
- 52
- 26
- 2 × 13
- 27
- 33
- 28
- 22 × 7
- 29
- prime
- 30
- 2 × 3 × 5
- 31
- prime
- 32
- 25
- 33
- 3 × 11
- 34
- 2 × 17
- 35
- 5 × 7
- 36
- 22 × 32
- 37
- prime
- 38
- 2 × 19
- 39
- 3 × 13
- 40
- 23 × 5
- 41
- prime
- 42
- 2 × 3 × 7
- 43
- prime
- 44
- 22 × 11
- 45
- 32 × 5
- 46
- 2 × 23
- 47
- prime
- 48
- 24 × 3
- 49
- 72
- 50
- 2 × 52
- 51
- 3 × 17
- 52
- 22 × 13
- 53
- prime
- 54
- 2 × 33
- 55
- 5 × 11
- 56
- 23 × 7
- 57
- 3 × 19
- 58
- 2 × 29
- 59
- prime
- 60
- 22 × 3 × 5
- 61
- prime
- 62
- 2 × 31
- 63
- 32 × 7
- 64
- 26
- 65
- 5 × 13
- 66
- 2 × 3 × 11
- 67
- prime
- 68
- 22 × 17
- 69
- 3 × 23
- 70
- 2 × 5 × 7
- 71
- prime
- 72
- 23 × 32
- 73
- prime
- 74
- 2 × 37
- 75
- 3 × 52
- 76
- 22 × 19
- 77
- 7 × 11
- 78
- 2 × 3 × 13
- 79
- prime
- 80
- 24 × 5
- 81
- 34
- 82
- 2 × 41
- 83
- prime
- 84
- 22 × 3 × 7
- 85
- 5 × 17
- 86
- 2 × 43
- 87
- 3 × 29
- 88
- 23 × 11
- 89
- prime
- 90
- 2 × 32 × 5
- 91
- 7 × 13
- 92
- 22 × 23
- 93
- 3 × 31
- 94
- 2 × 47
- 95
- 5 × 19
- 96
- 25 × 3
- 97
- prime
- 98
- 2 × 72
- 99
- 32 × 11
- 100
- 22 × 52
Benefits
Why prime factorization is worth knowing
Simplify fractions
Cancel shared primes from the top and bottom to reduce any fraction to its simplest form.
Find the LCM and GCF
Compare factorizations: the GCF uses the lowest powers of shared primes, the LCM the highest powers of all primes.
Simplify square roots
Pull pairs of primes outside the root, for example √72 = √(23·32) = 6√2.
Understand encryption
RSA security relies on the fact that multiplying two huge primes is easy, but factoring the result is extremely hard.
Check your homework
Compare each step of your factor tree or ladder with ours to spot exactly where a mistake crept in.
Solve number puzzles
Coding challenges and puzzle books often ask for the largest prime factor or number of divisors, which you get here instantly.
FAQ
Prime factorization FAQ
What is prime factorization?
Prime factorization means writing a whole number as a product of prime numbers, for example 360 = 2³ × 3² × 5. Every whole number greater than 1 has exactly one prime factorization, apart from the order of the factors. This is known as the fundamental theorem of arithmetic.
How do you find the prime factorization of a number?
Divide the number by the smallest prime that goes in evenly, then repeat with the answer until you reach 1. The primes you divided by are the prime factors. A factor tree does the same job by splitting the number into any two factors until every branch ends in a prime.
Is 1 a prime number?
No. A prime number has exactly two different factors, 1 and itself. The number 1 has only one factor, so it is neither prime nor composite and it has no prime factorization.
What is a factor tree?
A factor tree is a diagram that splits a number into two factors, then splits each composite factor again until only primes are left at the ends of the branches. Different trees for the same number always finish with the same set of primes.
How do you find the number of factors from the prime factorization?
Add 1 to each exponent in the prime factorization and multiply the results. For example, 360 = 2³ × 3² × 5¹, so it has (3 + 1)(2 + 1)(1 + 1) = 24 factors.
What is the largest number this calculator can factor?
It factors any whole number up to 9,007,199,254,740,991, which is 2⁵³ − 1 and the largest integer a browser can store exactly. Even near that limit, the result usually appears in well under a second.
What is the difference between factors and prime factors?
Factors are all the whole numbers that divide a number exactly, while prime factors are only the primes among them. For example, 360 has 24 factors, but its prime factors are just 2, 3 and 5.
What are perfect, abundant and deficient numbers?
Add up all the factors of a number except the number itself. If the total equals the number, it is perfect, like 6 and 28. If the total is bigger, it is abundant, like 12. If it is smaller, it is deficient, which includes every prime number.
Break any number into primes
Use the prime factorization calculator for homework, puzzles or curiosity, and see the tree, the steps and every factor at once. For more maths help, explore our free online tools.
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