What is the Greatest Common Factor of 83754 and 83772?

Greatest common factor (GCF) of 83754 and 83772 is 18.

GCF(83754,83772) = 18

We will now calculate the prime factors of 83754 and 83772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83754 and 83772.

How to find the GCF of 83754 and 83772?

We will first find the prime factorization of 83754 and 83772. After we will calculate the factors of 83754 and 83772 and find the biggest common factor number .

Step-1: Prime Factorization of 83754

Prime factors of 83754 are 2, 3, 11, 47. Prime factorization of 83754 in exponential form is:

83754 = 2¹ × 3⁴ × 11¹ × 47¹

Step-2: Prime Factorization of 83772

Prime factors of 83772 are 2, 3, 13, 179. Prime factorization of 83772 in exponential form is:

83772 = 2² × 3² × 13¹ × 179¹

Step-3: Factors of 83754

List of positive integer factors of 83754 that divides 83754 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 47, 54, 66, 81, 94, 99, 141, 162, 198, 282, 297, 423, 517, 594, 846, 891, 1034, 1269, 1551, 1782, 2538, 3102, 3807, 4653, 7614, 9306, 13959, 27918, 41877

Step-4: Factors of 83772

List of positive integer factors of 83772 that divides 83754 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 179, 234, 358, 468, 537, 716, 1074, 1611, 2148, 2327, 3222, 4654, 6444, 6981, 9308, 13962, 20943, 27924, 41886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83754 and 83772. The biggest common factor number is the GCF number.
So the greatest common factor 83754 and 83772 is 18.

Also check out the Least Common Multiple of 83754 and 83772