What is the Greatest Common Factor of 83664 and 83678?

Greatest common factor (GCF) of 83664 and 83678 is 14.

GCF(83664,83678) = 14

We will now calculate the prime factors of 83664 and 83678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83664 and 83678.

How to find the GCF of 83664 and 83678?

We will first find the prime factorization of 83664 and 83678. After we will calculate the factors of 83664 and 83678 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 83678

Prime factors of 83678 are 2, 7, 43, 139. Prime factorization of 83678 in exponential form is:

83678 = 2¹ × 7¹ × 43¹ × 139¹

Step-3: Factors of 83664

List of positive integer factors of 83664 that divides 83664 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

Step-4: Factors of 83678

List of positive integer factors of 83678 that divides 83664 without a remainder.

1, 2, 7, 14, 43, 86, 139, 278, 301, 602, 973, 1946, 5977, 11954, 41839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83664 and 83678. The biggest common factor number is the GCF number.
So the greatest common factor 83664 and 83678 is 14.

Also check out the Least Common Multiple of 83664 and 83678