What is the Greatest Common Factor of 39760 and 39774?

Greatest common factor (GCF) of 39760 and 39774 is 14.

GCF(39760,39774) = 14

We will now calculate the prime factors of 39760 and 39774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39760 and 39774.

How to find the GCF of 39760 and 39774?

We will first find the prime factorization of 39760 and 39774. After we will calculate the factors of 39760 and 39774 and find the biggest common factor number .

Step-1: Prime Factorization of 39760

Prime factors of 39760 are 2, 5, 7, 71. Prime factorization of 39760 in exponential form is:

39760 = 2⁴ × 5¹ × 7¹ × 71¹

Step-2: Prime Factorization of 39774

Prime factors of 39774 are 2, 3, 7, 947. Prime factorization of 39774 in exponential form is:

39774 = 2¹ × 3¹ × 7¹ × 947¹

Step-3: Factors of 39760

List of positive integer factors of 39760 that divides 39760 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 71, 80, 112, 140, 142, 280, 284, 355, 497, 560, 568, 710, 994, 1136, 1420, 1988, 2485, 2840, 3976, 4970, 5680, 7952, 9940, 19880

Step-4: Factors of 39774

List of positive integer factors of 39774 that divides 39760 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 947, 1894, 2841, 5682, 6629, 13258, 19887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39760 and 39774. The biggest common factor number is the GCF number.
So the greatest common factor 39760 and 39774 is 14.

Also check out the Least Common Multiple of 39760 and 39774