What is the Greatest Common Factor of 34706 and 34720?

Greatest common factor (GCF) of 34706 and 34720 is 14.

GCF(34706,34720) = 14

We will now calculate the prime factors of 34706 and 34720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34706 and 34720.

How to find the GCF of 34706 and 34720?

We will first find the prime factorization of 34706 and 34720. After we will calculate the factors of 34706 and 34720 and find the biggest common factor number .

Step-1: Prime Factorization of 34706

Prime factors of 34706 are 2, 7, 37, 67. Prime factorization of 34706 in exponential form is:

34706 = 2¹ × 7¹ × 37¹ × 67¹

Step-2: 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-3: Factors of 34706

List of positive integer factors of 34706 that divides 34706 without a remainder.

1, 2, 7, 14, 37, 67, 74, 134, 259, 469, 518, 938, 2479, 4958, 17353

Step-4: Factors of 34720

List of positive integer factors of 34720 that divides 34706 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34706 and 34720. The biggest common factor number is the GCF number.
So the greatest common factor 34706 and 34720 is 14.

Also check out the Least Common Multiple of 34706 and 34720