What is the Greatest Common Factor of 34720 and 34740?

Greatest common factor (GCF) of 34720 and 34740 is 20.

GCF(34720,34740) = 20

We will now calculate the prime factors of 34720 and 34740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34720 and 34740.

How to find the GCF of 34720 and 34740?

We will first find the prime factorization of 34720 and 34740. After we will calculate the factors of 34720 and 34740 and find the biggest common factor number .

Step-1: Prime Factorization of 34720

Prime factors of 34720 are 2, 5, 7, 31. Prime factorization of 34720 in exponential form is:

34720 = 2⁵ × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 34740

Prime factors of 34740 are 2, 3, 5, 193. Prime factorization of 34740 in exponential form is:

34740 = 2² × 3² × 5¹ × 193¹

Step-3: Factors of 34720

List of positive integer factors of 34720 that divides 34720 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 31, 32, 35, 40, 56, 62, 70, 80, 112, 124, 140, 155, 160, 217, 224, 248, 280, 310, 434, 496, 560, 620, 868, 992, 1085, 1120, 1240, 1736, 2170, 2480, 3472, 4340, 4960, 6944, 8680, 17360

Step-4: Factors of 34740

List of positive integer factors of 34740 that divides 34720 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 193, 386, 579, 772, 965, 1158, 1737, 1930, 2316, 2895, 3474, 3860, 5790, 6948, 8685, 11580, 17370

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34720 and 34740. The biggest common factor number is the GCF number.
So the greatest common factor 34720 and 34740 is 20.

Also check out the Least Common Multiple of 34720 and 34740