What is the Greatest Common Factor of 77112 and 77126?

Greatest common factor (GCF) of 77112 and 77126 is 14.

GCF(77112,77126) = 14

We will now calculate the prime factors of 77112 and 77126, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77112 and 77126.

How to find the GCF of 77112 and 77126?

We will first find the prime factorization of 77112 and 77126. After we will calculate the factors of 77112 and 77126 and find the biggest common factor number .

Step-1: Prime Factorization of 77112

Prime factors of 77112 are 2, 3, 7, 17. Prime factorization of 77112 in exponential form is:

77112 = 2³ × 3⁴ × 7¹ × 17¹

Step-2: Prime Factorization of 77126

Prime factors of 77126 are 2, 7, 787. Prime factorization of 77126 in exponential form is:

77126 = 2¹ × 7² × 787¹

Step-3: Factors of 77112

List of positive integer factors of 77112 that divides 77112 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 17, 18, 21, 24, 27, 28, 34, 36, 42, 51, 54, 56, 63, 68, 72, 81, 84, 102, 108, 119, 126, 136, 153, 162, 168, 189, 204, 216, 238, 252, 306, 324, 357, 378, 408, 459, 476, 504, 567, 612, 648, 714, 756, 918, 952, 1071, 1134, 1224, 1377, 1428, 1512, 1836, 2142, 2268, 2754, 2856, 3213, 3672, 4284, 4536, 5508, 6426, 8568, 9639, 11016, 12852, 19278, 25704, 38556

Step-4: Factors of 77126

List of positive integer factors of 77126 that divides 77112 without a remainder.

1, 2, 7, 14, 49, 98, 787, 1574, 5509, 11018, 38563

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77112 and 77126. The biggest common factor number is the GCF number.
So the greatest common factor 77112 and 77126 is 14.

Also check out the Least Common Multiple of 77112 and 77126