What is the Greatest Common Factor of 29120 and 29140?

Greatest common factor (GCF) of 29120 and 29140 is 20.

GCF(29120,29140) = 20

We will now calculate the prime factors of 29120 and 29140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29120 and 29140.

How to find the GCF of 29120 and 29140?

We will first find the prime factorization of 29120 and 29140. After we will calculate the factors of 29120 and 29140 and find the biggest common factor number .

Step-1: Prime Factorization of 29120

Prime factors of 29120 are 2, 5, 7, 13. Prime factorization of 29120 in exponential form is:

29120 = 2⁶ × 5¹ × 7¹ × 13¹

Step-2: Prime Factorization of 29140

Prime factors of 29140 are 2, 5, 31, 47. Prime factorization of 29140 in exponential form is:

29140 = 2² × 5¹ × 31¹ × 47¹

Step-3: Factors of 29120

List of positive integer factors of 29120 that divides 29120 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 32, 35, 40, 52, 56, 64, 65, 70, 80, 91, 104, 112, 130, 140, 160, 182, 208, 224, 260, 280, 320, 364, 416, 448, 455, 520, 560, 728, 832, 910, 1040, 1120, 1456, 1820, 2080, 2240, 2912, 3640, 4160, 5824, 7280, 14560

Step-4: Factors of 29140

List of positive integer factors of 29140 that divides 29120 without a remainder.

1, 2, 4, 5, 10, 20, 31, 47, 62, 94, 124, 155, 188, 235, 310, 470, 620, 940, 1457, 2914, 5828, 7285, 14570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29120 and 29140. The biggest common factor number is the GCF number.
So the greatest common factor 29120 and 29140 is 20.

Also check out the Least Common Multiple of 29120 and 29140