What is the Greatest Common Factor of 27762 and 27776?

Greatest common factor (GCF) of 27762 and 27776 is 14.

GCF(27762,27776) = 14

We will now calculate the prime factors of 27762 and 27776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27762 and 27776.

How to find the GCF of 27762 and 27776?

We will first find the prime factorization of 27762 and 27776. After we will calculate the factors of 27762 and 27776 and find the biggest common factor number .

Step-1: Prime Factorization of 27762

Prime factors of 27762 are 2, 3, 7, 661. Prime factorization of 27762 in exponential form is:

27762 = 2¹ × 3¹ × 7¹ × 661¹

Step-2: Prime Factorization of 27776

Prime factors of 27776 are 2, 7, 31. Prime factorization of 27776 in exponential form is:

27776 = 2⁷ × 7¹ × 31¹

Step-3: Factors of 27762

List of positive integer factors of 27762 that divides 27762 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 661, 1322, 1983, 3966, 4627, 9254, 13881

Step-4: Factors of 27776

List of positive integer factors of 27776 that divides 27762 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 56, 62, 64, 112, 124, 128, 217, 224, 248, 434, 448, 496, 868, 896, 992, 1736, 1984, 3472, 3968, 6944, 13888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27762 and 27776. The biggest common factor number is the GCF number.
So the greatest common factor 27762 and 27776 is 14.

Also check out the Least Common Multiple of 27762 and 27776