What is the Greatest Common Factor of 83524 and 83538?

Greatest common factor (GCF) of 83524 and 83538 is 14.

GCF(83524,83538) = 14

We will now calculate the prime factors of 83524 and 83538, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83524 and 83538.

How to find the GCF of 83524 and 83538?

We will first find the prime factorization of 83524 and 83538. After we will calculate the factors of 83524 and 83538 and find the biggest common factor number .

Step-1: Prime Factorization of 83524

Prime factors of 83524 are 2, 7, 19, 157. Prime factorization of 83524 in exponential form is:

83524 = 2² × 7¹ × 19¹ × 157¹

Step-2: Prime Factorization of 83538

Prime factors of 83538 are 2, 3, 7, 13, 17. Prime factorization of 83538 in exponential form is:

83538 = 2¹ × 3³ × 7¹ × 13¹ × 17¹

Step-3: Factors of 83524

List of positive integer factors of 83524 that divides 83524 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 157, 266, 314, 532, 628, 1099, 2198, 2983, 4396, 5966, 11932, 20881, 41762

Step-4: Factors of 83538

List of positive integer factors of 83538 that divides 83524 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 17, 18, 21, 26, 27, 34, 39, 42, 51, 54, 63, 78, 91, 102, 117, 119, 126, 153, 182, 189, 221, 234, 238, 273, 306, 351, 357, 378, 442, 459, 546, 663, 702, 714, 819, 918, 1071, 1326, 1547, 1638, 1989, 2142, 2457, 3094, 3213, 3978, 4641, 4914, 5967, 6426, 9282, 11934, 13923, 27846, 41769

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83524 and 83538. The biggest common factor number is the GCF number.
So the greatest common factor 83524 and 83538 is 14.

Also check out the Least Common Multiple of 83524 and 83538