What is the Greatest Common Factor of 39748 and 39760?

Greatest common factor (GCF) of 39748 and 39760 is 4.

GCF(39748,39760) = 4

We will now calculate the prime factors of 39748 and 39760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39748 and 39760.

How to find the GCF of 39748 and 39760?

We will first find the prime factorization of 39748 and 39760. After we will calculate the factors of 39748 and 39760 and find the biggest common factor number .

Step-1: Prime Factorization of 39748

Prime factors of 39748 are 2, 19, 523. Prime factorization of 39748 in exponential form is:

39748 = 2² × 19¹ × 523¹

Step-2: 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-3: Factors of 39748

List of positive integer factors of 39748 that divides 39748 without a remainder.

1, 2, 4, 19, 38, 76, 523, 1046, 2092, 9937, 19874

Step-4: Factors of 39760

List of positive integer factors of 39760 that divides 39748 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39748 and 39760. The biggest common factor number is the GCF number.
So the greatest common factor 39748 and 39760 is 4.

Also check out the Least Common Multiple of 39748 and 39760