What is the Greatest Common Factor of 83657 and 83664?

Greatest common factor (GCF) of 83657 and 83664 is 7.

GCF(83657,83664) = 7

We will now calculate the prime factors of 83657 and 83664, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83657 and 83664.

How to find the GCF of 83657 and 83664?

We will first find the prime factorization of 83657 and 83664. After we will calculate the factors of 83657 and 83664 and find the biggest common factor number .

Step-1: Prime Factorization of 83657

Prime factors of 83657 are 7, 17, 19, 37. Prime factorization of 83657 in exponential form is:

83657 = 7¹ × 17¹ × 19¹ × 37¹

Step-2: Prime Factorization of 83664

Prime factors of 83664 are 2, 3, 7, 83. Prime factorization of 83664 in exponential form is:

83664 = 2⁴ × 3² × 7¹ × 83¹

Step-3: Factors of 83657

List of positive integer factors of 83657 that divides 83657 without a remainder.

1, 7, 17, 19, 37, 119, 133, 259, 323, 629, 703, 2261, 4403, 4921, 11951

Step-4: Factors of 83664

List of positive integer factors of 83664 that divides 83657 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 83, 84, 112, 126, 144, 166, 168, 249, 252, 332, 336, 498, 504, 581, 664, 747, 996, 1008, 1162, 1328, 1494, 1743, 1992, 2324, 2988, 3486, 3984, 4648, 5229, 5976, 6972, 9296, 10458, 11952, 13944, 20916, 27888, 41832

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83657 and 83664. The biggest common factor number is the GCF number.
So the greatest common factor 83657 and 83664 is 7.

Also check out the Least Common Multiple of 83657 and 83664