What is the Greatest Common Factor of 69875 and 69888?

Greatest common factor (GCF) of 69875 and 69888 is 13.

GCF(69875,69888) = 13

We will now calculate the prime factors of 69875 and 69888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69875 and 69888.

How to find the GCF of 69875 and 69888?

We will first find the prime factorization of 69875 and 69888. After we will calculate the factors of 69875 and 69888 and find the biggest common factor number .

Step-1: Prime Factorization of 69875

Prime factors of 69875 are 5, 13, 43. Prime factorization of 69875 in exponential form is:

69875 = 5³ × 13¹ × 43¹

Step-2: 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-3: Factors of 69875

List of positive integer factors of 69875 that divides 69875 without a remainder.

1, 5, 13, 25, 43, 65, 125, 215, 325, 559, 1075, 1625, 2795, 5375, 13975

Step-4: Factors of 69888

List of positive integer factors of 69888 that divides 69875 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69875 and 69888. The biggest common factor number is the GCF number.
So the greatest common factor 69875 and 69888 is 13.

Also check out the Least Common Multiple of 69875 and 69888