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