# Prime Factorization

## What is prime factorization?

“Prime factorization” is finding which prime numbers multiply to make the original number.

The prime factorization of 5 is 1 × 5. The number 5 is a prime number, because its only factors are 1 and itself.

What is PRIME number?
Some number can only be divided by 1 or the number itself. These numbers are called prime numbers. Eg. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc.

## How to find the prime factorization?

Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are prime numbers.

TIPS: Try to keep tables (at least till 20) on your finger tips. Revise tables every day

## Prime factorization of common numbers

Prime factorization of 2: prime number
Prime factorization of 3: prime number
Prime factorization of 4: 2 x 2
Prime factorization of 5: prime number
Prime factorization of 6: 2 × 3
Prime factorization of 7: prime number
Prime factorization of 8: 2 x 2 x 2
Prime factorization of 9: 3 x 3
Prime factorization of 10: 2 × 5
Prime factorization of 11: prime number
Prime factorization of 12: 2 x 2 × 3
Prime factorization of 13: prime number
Prime factorization of 14: 2 × 7
Prime factorization of 15: 3 × 5
Prime factorization of 16: 2 x 2 x 2 x 2
Prime factorization of 17: prime number
Prime factorization of 18: 2 × 3 x 3
Prime factorization of 19: prime number
Prime factorization of 20: 2 x 2 × 5
Prime factorization of 21: 3 × 7
Prime factorization of 22: 2 × 11
Prime factorization of 23: prime number
Prime factorization of 24: 2 x 2 x 2 × 3
Prime factorization of 25: 5 x 5

Prime factorization of 26: 2 × 13
Prime factorization of 27: 3 x 3 x 3
Prime factorization of 28: 2 x 2 × 7
Prime factorization of 29: prime number
Prime factorization of 30: 2 × 3 × 5
Prime factorization of 31: prime number
Prime factorization of 32: 2 x 2 x 2 x 2 x 2
Prime factorization of 33: 3 × 11
Prime factorization of 34: 2 × 17
Prime factorization of 35: 5 × 7
Prime factorization of 36: 2 x 2 × 3 x 3
Prime factorization of 37: prime number
Prime factorization of 38: 2 × 19
Prime factorization of 39: 3 × 13
Prime factorization of 40: 2 x 2 x 2 × 5
Prime factorization of 41: prime number
Prime factorization of 42: 2 × 3 × 7
Prime factorization of 43: prime number
Prime factorization of 44: 2 x 2 × 11
Prime factorization of 45: 3 x 3 × 5
Prime factorization of 46: 2 × 23
Prime factorization of 47: prime number
Prime factorization of 48: 2 x 2 x 2 x 2 × 3
Prime factorization of 49: 7 x 7
Prime factorization of 50: 2 × 5 x 5

Prime factorization of 51: 3 × 17
Prime factorization of 52: 2 x 2 × 13
Prime factorization of 53: prime number
Prime factorization of 54: 2 × 3 x 3 x 3
Prime factorization of 55: 5 × 11
Prime factorization of 56: 2 x 2 x 2 × 7
Prime factorization of 57: 3 × 19
Prime factorization of 58: 2 × 29
Prime factorization of 59: prime number
Prime factorization of 60: 2 x 2 × 3 × 5
Prime factorization of 61: prime number
Prime factorization of 62: 2 × 31
Prime factorization of 63: 3 x 3 × 7
Prime factorization of 64: 2 x 2 x 2 x 2 x 2 x 2
Prime factorization of 65: 5 × 13
Prime factorization of 66: 2 × 3 × 11
Prime factorization of 67: prime number
Prime factorization of 68: 2 x 2 × 17
Prime factorization of 69: 3 × 23
Prime factorization of 70: 2 × 5 × 7
Prime factorization of 71: prime number
Prime factorization of 72: 2 x 2 x 2 × 3 x 3
Prime factorization of 73: prime number
Prime factorization of 74: 2 × 37
Prime factorization of 75: 3 × 5 x 5

Prime factorization of 76: 2 x 2 × 19
Prime factorization of 77: 7 × 11
Prime factorization of 78: 2 × 3 × 13
Prime factorization of 79: prime number
Prime factorization of 80: 2 x 2 x 2 x 2 × 5
Prime factorization of 81: 3 x 3 x 3 x 3
Prime factorization of 82: 2 × 41
Prime factorization of 83: prime number
Prime factorization of 84: 2 x 2 × 3 × 7
Prime factorization of 85: 5 × 17
Prime factorization of 86: 2 × 43
Prime factorization of 87: 3 × 29
Prime factorization of 88: 2 x 2 x 2 × 11
Prime factorization of 89: prime number
Prime factorization of 90: 2 × 3 x 3 × 5
Prime factorization of 91: 7 × 13
Prime factorization of 92: 2 x 2 × 23
Prime factorization of 93: 3 × 31
Prime factorization of 94: 2 × 47
Prime factorization of 95: 5 × 19
Prime factorization of 96: 2 x 2 x 2 x 2 x 2 × 3
Prime factorization of 97: prime number
Prime factorization of 98: 2 × 7 x 7
Prime factorization of 99: 3 x 3 × 11
Prime factorization of 100: 2 x 2 × 5 x 5

Prime factorization of 101: prime number
Prime factorization of 102: 2 × 3 × 17
Prime factorization of 103: prime number
Prime factorization of 104: 2 x 2 x 2 × 13
Prime factorization of 105: 3 × 5 × 7
Prime factorization of 106: 2 × 53
Prime factorization of 107: prime number
Prime factorization of 108: 2 x 2 × 3 x 3 x 3
Prime factorization of 109: prime number
Prime factorization of 110: 2 × 5 × 11
Prime factorization of 111: 3 × 37
Prime factorization of 112: 2 x 2 x 2 x 2 × 7
Prime factorization of 113: prime number
Prime factorization of 114: 2 × 3 × 19
Prime factorization of 115: 5 × 23
Prime factorization of 116:  2 x 2 × 29
Prime factorization of 117: 3 x 3 × 13
Prime factorization of 118: 2 × 59
Prime factorization of 119: 7 × 17
Prime factorization of 120: 2 x 2 x 2 × 3 × 5
Prime factorization of 121: 11 x 11
Prime factorization of 122: 2 × 61
Prime factorization of 123: 3 × 41
Prime factorization of 124: 2 x 2 × 31
Prime factorization of 125: 5 x 5 x 5
Prime factorization of 126: 2 × 3 x 3 × 7
Prime factorization of 127: prime number
Prime factorization of 128: 2 x 2 x 2 x 2 x 2 x 2 x 2
Prime factorization of 129: 3 × 43
Prime factorization of 130: 2 × 5 × 13
Prime factorization of 131: prime number
Prime factorization of 132: 2 x 2 × 3 × 11
Prime factorization of 133: 7 × 19
Prime factorization of 134: 2 × 67
Prime factorization of 135: 3 x 3 x 3 × 5
Prime factorization of 136: 2 x 2 x 2 × 17
Prime factorization of 137: prime number
Prime factorization of 138: 2 × 3 × 23
Prime factorization of 139: prime number
Prime factorization of 140: 2 x 2 × 5 × 7
Prime factorization of 141: 3 × 47
Prime factorization of 142: 2 × 71
Prime factorization of 143: 11 × 13
Prime factorization of 144: 2 x 2 x 2 x 2 × 3 x 3
Prime factorization of 145: 5 × 29
Prime factorization of 146: 2 × 73
Prime factorization of 147: 3 × 7 x 7
Prime factorization of 148: 2 x 2 × 37
Prime factorization of 149: prime number
Prime factorization of 150: 2 × 3 × 5 x 5

Prime factorization of 200: 2 x 2 x 2 × 5 x 5
Prime factorization of 300: 2 x 2 × 3 × 5 x 5
Prime factorization of 400: 2 x 2 x 2 x 2 × 5 x 5
Prime factorization of 500: 2 x 2 × 5 x 5 x 5
Prime factorization of 600: 2 x 2 x 2 × 3 × 5 x 5
Prime factorization of 700: 2 x 2 × 5 x 5 × 7
Prime factorization of 800: 2 x 2 x 2 x 2 x 2 × 5 x 5
Prime factorization of 900: 2 x 2 × 3 x 3 × 5 x 5
Prime factorization of 1000: 2 x 2 x 2 × 5 x 5 x 5

Translate »
Scroll to Top