What is the Greatest Common Factor of 69538 and 69552?

Greatest common factor (GCF) of 69538 and 69552 is 14.

GCF(69538,69552) = 14

We will now calculate the prime factors of 69538 and 69552, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69538 and 69552.

How to find the GCF of 69538 and 69552?

We will first find the prime factorization of 69538 and 69552. After we will calculate the factors of 69538 and 69552 and find the biggest common factor number .

Step-1: Prime Factorization of 69538

Prime factors of 69538 are 2, 7, 4967. Prime factorization of 69538 in exponential form is:

69538 = 2¹ × 7¹ × 4967¹

Step-2: Prime Factorization of 69552

Prime factors of 69552 are 2, 3, 7, 23. Prime factorization of 69552 in exponential form is:

69552 = 2⁴ × 3³ × 7¹ × 23¹

Step-3: Factors of 69538

List of positive integer factors of 69538 that divides 69538 without a remainder.

1, 2, 7, 14, 4967, 9934, 34769

Step-4: Factors of 69552

List of positive integer factors of 69552 that divides 69538 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 23, 24, 27, 28, 36, 42, 46, 48, 54, 56, 63, 69, 72, 84, 92, 108, 112, 126, 138, 144, 161, 168, 184, 189, 207, 216, 252, 276, 322, 336, 368, 378, 414, 432, 483, 504, 552, 621, 644, 756, 828, 966, 1008, 1104, 1242, 1288, 1449, 1512, 1656, 1932, 2484, 2576, 2898, 3024, 3312, 3864, 4347, 4968, 5796, 7728, 8694, 9936, 11592, 17388, 23184, 34776

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69538 and 69552. The biggest common factor number is the GCF number.
So the greatest common factor 69538 and 69552 is 14.

Also check out the Least Common Multiple of 69538 and 69552