The element factorization calculator will certainly take any kind of number and also find its element factors. Simply kind the number right into our tool and also in no time you'll find the prime factorization. To recognize the totality process, very first you should get acquainted with what is a element factor. As soon as you know that, we will relocate on to the difference in between prime factor and prime factorization.

You are watching: 20 as a product of prime factors

Below, you'll discover all the answers, and also concise information about how to uncover prime factorization and also what a variable tree is.

## What is a element number?

To know prime factorization, we should start from the start - what is a prime number? A prime numbers are numbers who only determinants are one and also itself - in other words, it can't be developed by multiplying two smaller organic numbers. A crucial point to keep in mind is that the two factors must be different, so 1 is not a element number since both components of 1 are the same. Because that example, 5 is a element number since the only components of 5 space 1 and also 5. 6 is no a element as, apart from 1 and also 6, other factors exist - 2 and also 3.

There are infinitely many primes and also there's no simple formula to recognize whether a number is a prime or not. That's why this prime factorization calculator is such a great, multi-purpose tool - you have the right to use it together a prime number calculator together well!

## What is a element factor?

Prime factors are determinants of a number that room themselves prime numbers. Because that example, suppose we desire to find the factors of 20, that is, we desire to recognize what totality numbers main point to give you 20. We know that 1 * 20 = 20, 2 * 10 = 20 and also 4 * 5 = 20. But notification that 20, 10 and 4 room not prime factors. The only prime determinants of 20 are 2 and also 5. Friend can additionally get these components with the usage of our aspect calculator.

## What is element factorization?

Prime administer is when we rest a number under into factors that are just prime numbers. If we look in ~ the over example v 20, the determinants are 1, 2, 4, 5, 10, 20. The ideal place to begin is to uncover at the very least one initial factor that is prime. Since 5 is prime, we deserve to start v 4 * 5. An alert that 4 is not prime, so us break 4 down right into 2 * 2. Because 2 is prime, the element factorization that 20 is 2 * 2 * 5. Walk ahead and check this result with our element factorization calculator.

## How to discover prime factorization? A factor tree method

We'll present you action by step exactly how to uncover prime factorization. We'll usage the aspect tree diagram, one easy means to failure a number into its prime factors. Are you ready?

Take a number. There's no point in picking a prime number, together the prime factorization will end up at this point. Let's choose 36.Factor it into any kind of two numbers, prime or not. You might want to take it the easiest splits, e.g., if your number is even, split it into 2 and also the other number. 36 is also so that we can write it as 2 * 18.Start constructing the aspect tree. Attract two branches splitting down from your initial number.

Factor the following line. If your number is a prime, leave it as it is. If it's not a prime number, repeat action 2.
Repeat step 4 until you're left with just prime numbers.
Write down the last prime factorization and also prime factors.
Take every the "leaves" of your aspect tree and also multiply them together:

36 = 2 * 2 * 3 * 3

That's just how we discover prime factorization!

The prime factors that our original number 36 are 2 and also 3. The same prime element may occur an ext than once, i beg your pardon is precisely what occurred in our case - both element numbers show up twice in the prime factorization. We have the right to then express it as:

36 = 2² * 3²

Of course, girlfriend should get the same an outcome with a various factor tree splits, together e.g. Here:

## Greatest common Factor

Prime administrate is the very first step in detect the greatest common factor - the greatest element of two or much more numbers. The GCF is especially valuable for simple fractions and also solving equations making use of polynomials. Because that example, the greatest usual factor in between 6 and also 20 is 2: element factorization of the an initial number is 6 = 2 * 3, the last may it is in expressed as 20 = 5 * 2 * 2, and the just number which shows up in both prime factorizations is 2, indeed. If you desire to calculation greatest typical factor in a snap, use our greatest common factor calculator.

## Least usual Multiple

The the prime factorization calculator is also useful in finding the least usual multiple (LCM). The LCM is necessary when adding fractions with various denominators. The least typical multiple is derived when you main point the greater powers of all factors between the two numbers. For example, the least common multiple in between 6 and 20 is (2 * 2 * 3 * 5) = 60. The LCM may be discovered by hand or through use that the least typical multiple calculator.

## What is prime factorization of...

Notice the list of element factorizations below, which deserve to be checked using our prime factorization calculator.

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Prime administer of 2: it's a prime number!

Prime factorization of 3: it's a element number!

Prime factorization of 4: 2 * 2

Prime administrate of 5: it's a element number!

Prime administer of 6: 2 * 3

Prime administer of 7: it's a element number!

Prime administrate of 8: 2 * 2 * 2

Prime factorization of 9: 3 * 3

Prime administer of 10: 2 * 5

Prime factorization of 11: it's a element number!

Prime administrate of 12: 2 * 2 * 3

Prime administrate of 13: it's a element number!

Prime administrate of 14: 2 * 7

Prime administrate of 15: 3 * 5

Prime administrate of 16: 2 * 2 * 2 * 2

Prime factorization of 17: it's a element number!

Prime administrate of 18: 2 * 3 * 3

Prime administer of 19: it's a prime number!

Prime administrate of 20: 2 * 2 * 5

Prime administrate of 21: 3 * 7

Prime factorization of 22: 2 * 11

Prime factorization of 23: it's a element number!

Prime factorization of 24: 2 * 2 * 2 * 3

Prime administrate of 25: 5 * 5

Prime administer of 26: 2 * 13

Prime administer of 27: 3 * 3 * 3

Prime administrate of 28: 2 * 2 * 7

Prime administrate of 29: it's a element number!

Prime factorization of 30: 2 * 3 * 5

Prime administrate of 31: it's a prime number!

Prime administrate of 32: 2 * 2 * 2 * 2 * 2

Prime administer of 33: 3 * 11

Prime administer of 34: 2 * 17

Prime administer of 35: 5 * 7

Prime factorization of 36: 2 * 2 * 3 * 3

Prime administer of 37: it's a prime number!

Prime administer of 38: 2 * 19

Prime administrate of 39: 3 * 13

Prime administer of 40: 2 * 2 * 2 * 5

Prime administer of 41: it's a prime number!

Prime factorization of 42: 2 * 3 * 7

Prime administrate of 43: it's a prime number!

Prime administer of 44: 2 * 2 * 11

Prime administer of 45: 3 * 3 * 5

Prime administer of 46: 2 * 23

Prime administer of 47: it's a element number!

Prime administer of 48: 2 * 2 * 2 * 2 * 3

Prime administrate of 49: 7 * 7

Prime administrate of 50: 2 * 5 * 5

Prime administer of 51: 3 * 17

Prime administer of 52: 2 * 2 * 13

Prime administrate of 53: it's a element number!

Prime factorization of 54: 2 * 3 * 3 * 3

Prime factorization of 55: 5 * 11

Prime administrate of 56: 2 * 2 * 2 * 7

Prime factorization of 57: 3 * 19

Prime administrate of 58: 2 * 29

Prime administer of 59: it's a prime number!

Prime factorization of 60: 2 * 2 * 3 * 5

Prime factorization of 61: it's a element number!

Prime administer of 62: 2 * 31

Prime administer of 63: 3 * 3 * 7

Prime administer of 64: 2 * 2 * 2 * 2 * 2 * 2

Prime factorization of 65: 5 * 13

Prime administrate of 66: 2 * 3 * 11

Prime administrate of 67: it's a element number!

Prime administer of 68: 2 * 2 * 17

Prime administer of 69: 3 * 23

Prime factorization of 70: 2 * 5 * 7

Prime administrate of 71: it's a element number!

Prime administrate of 72: 2 * 2 * 2 * 3 * 3

Prime administer of 73: it's a prime number!

Prime administer of 74: 2 * 37

Prime factorization of 75: 3 * 5 * 5

Prime factorization of 76: 2 * 2 * 19

Prime administer of 77: 7 * 11

Prime factorization of 78: 2 * 3 * 13

Prime administrate of 79: it's a element number!

Prime administer of 80: 2 * 2 * 2 * 2 * 5

Prime factorization of 81: 3 * 3 * 3 * 3

Prime factorization of 82: 2 * 41

Prime administer of 83: it's a prime number!

Prime administer of 84: 2 * 2 * 3 * 7

Prime factorization of 85: 5 * 17

Prime administrate of 86: 2 * 43

Prime administer of 87: 3 * 29

Prime administer of 88: 2 * 2 * 2 * 11

Prime administrate of 89: it's a prime number!

Prime administrate of 90: 2 * 3 * 3 * 5

Prime administer of 91: 7 * 13

Prime factorization of 92: 2 * 2 * 23

Prime factorization of 93: 3 * 31

Prime administer of 94: 2 * 47

Prime factorization of 95: 5 * 19

Prime administer of 96: 2 * 2 * 2 * 2 * 2 * 3

Prime factorization of 97: it's a element number!

Prime factorization of 98: 2 * 7 * 7

Prime administrate of 99: 3 * 3 * 11

Prime factorization of 100: 2 * 2 * 5 * 5

Prime factorization of 104: 2 * 2 * 2 * 13

Prime administer of 105: 3 * 5 * 7

Prime administrate of 108: 2 * 2 * 3 * 3 * 3

Prime administrate of 117: 3 * 3 * 13

Prime factorization of 120: 2 * 2 * 2 * 3 * 5

Prime administer of 121: 11 * 11

Prime administer of 125: 5 * 5 * 5

Prime administer of 126: 2 * 3 * 3 * 7

Prime administer of 130: 2 * 5 * 13

Prime administrate of 132: 2 * 2 * 3 * 11

Prime factorization of 135: 3 * 3 * 3 * 5

Prime administer of 140: 2 * 2 * 5 * 7

Prime administrate of 144: 2 * 2 * 2 * 2 * 3 * 3

Prime administrate of 147: 3 * 7 * 7

Prime factorization of 150: 2 * 3 * 5 * 5

Prime administer of 162: 2 * 3 * 3 * 3 * 3

Prime administrate of 175: 5 * 5 * 7

Prime administrate of 180: 2 * 2 * 3 * 3 * 5

Prime factorization of 196: 2 * 2 * 7 * 7

Prime administer of 200: 2 * 2 * 2 * 5 * 5

Prime administrate of 210: 2 * 3 * 5 * 7

Prime administer of 216: 2 * 2 * 2 * 3 * 3 * 3

Prime factorization of 225: 3 * 3 * 5 * 5

Prime administrate of 245: 5 * 7 * 7

Prime factorization of 250: 2 * 5 * 5 * 5

Prime administer of 256: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

Prime factorization of 300: 2 * 2 * 3 * 5 * 5

Prime factorization of 375: 3 * 5 * 5 * 5

Prime factorization of 400: 2 * 2 * 2 * 2 * 5 * 5

Prime administer of 500: 2 * 2 * 5 * 5 * 5

Prime factorization of 625: 5 * 5 * 5 * 5

At the beginning, 1 was considered a prime number. It to be not till the early 20th century that most mathematicians exclude, 1 as a prime number. Notice the prime factorization calculator go not incorporate 1 in the results of prime numbers.