What is the Greatest Common Factor of 37772 and 37786?

Greatest common factor (GCF) of 37772 and 37786 is 14.

GCF(37772,37786) = 14

We will now calculate the prime factors of 37772 and 37786, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37772 and 37786.

How to find the GCF of 37772 and 37786?

We will first find the prime factorization of 37772 and 37786. After we will calculate the factors of 37772 and 37786 and find the biggest common factor number .

Step-1: Prime Factorization of 37772

Prime factors of 37772 are 2, 7, 19, 71. Prime factorization of 37772 in exponential form is:

37772 = 2² × 7¹ × 19¹ × 71¹

Step-2: Prime Factorization of 37786

Prime factors of 37786 are 2, 7, 2699. Prime factorization of 37786 in exponential form is:

37786 = 2¹ × 7¹ × 2699¹

Step-3: Factors of 37772

List of positive integer factors of 37772 that divides 37772 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 71, 76, 133, 142, 266, 284, 497, 532, 994, 1349, 1988, 2698, 5396, 9443, 18886

Step-4: Factors of 37786

List of positive integer factors of 37786 that divides 37772 without a remainder.

1, 2, 7, 14, 2699, 5398, 18893

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37772 and 37786. The biggest common factor number is the GCF number.
So the greatest common factor 37772 and 37786 is 14.

Also check out the Least Common Multiple of 37772 and 37786