What is the Greatest Common Factor of 69888 and 69900?

Greatest common factor (GCF) of 69888 and 69900 is 12.

GCF(69888,69900) = 12

We will now calculate the prime factors of 69888 and 69900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69888 and 69900.

How to find the GCF of 69888 and 69900?

We will first find the prime factorization of 69888 and 69900. After we will calculate the factors of 69888 and 69900 and find the biggest common factor number .

Step-1: Prime Factorization of 69888

Prime factors of 69888 are 2, 3, 7, 13. Prime factorization of 69888 in exponential form is:

69888 = 2⁸ × 3¹ × 7¹ × 13¹

Step-2: Prime Factorization of 69900

Prime factors of 69900 are 2, 3, 5, 233. Prime factorization of 69900 in exponential form is:

69900 = 2² × 3¹ × 5² × 233¹

Step-3: Factors of 69888

List of positive integer factors of 69888 that divides 69888 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 16, 21, 24, 26, 28, 32, 39, 42, 48, 52, 56, 64, 78, 84, 91, 96, 104, 112, 128, 156, 168, 182, 192, 208, 224, 256, 273, 312, 336, 364, 384, 416, 448, 546, 624, 672, 728, 768, 832, 896, 1092, 1248, 1344, 1456, 1664, 1792, 2184, 2496, 2688, 2912, 3328, 4368, 4992, 5376, 5824, 8736, 9984, 11648, 17472, 23296, 34944

Step-4: Factors of 69900

List of positive integer factors of 69900 that divides 69888 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 233, 300, 466, 699, 932, 1165, 1398, 2330, 2796, 3495, 4660, 5825, 6990, 11650, 13980, 17475, 23300, 34950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69888 and 69900. The biggest common factor number is the GCF number.
So the greatest common factor 69888 and 69900 is 12.

Also check out the Least Common Multiple of 69888 and 69900