What is the Greatest Common Factor of 29945 and 29960?

Greatest common factor (GCF) of 29945 and 29960 is 5.

GCF(29945,29960) = 5

We will now calculate the prime factors of 29945 and 29960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29945 and 29960.

How to find the GCF of 29945 and 29960?

We will first find the prime factorization of 29945 and 29960. After we will calculate the factors of 29945 and 29960 and find the biggest common factor number .

Step-1: Prime Factorization of 29945

Prime factors of 29945 are 5, 53, 113. Prime factorization of 29945 in exponential form is:

29945 = 5¹ × 53¹ × 113¹

Step-2: Prime Factorization of 29960

Prime factors of 29960 are 2, 5, 7, 107. Prime factorization of 29960 in exponential form is:

29960 = 2³ × 5¹ × 7¹ × 107¹

Step-3: Factors of 29945

List of positive integer factors of 29945 that divides 29945 without a remainder.

1, 5, 53, 113, 265, 565, 5989

Step-4: Factors of 29960

List of positive integer factors of 29960 that divides 29945 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 107, 140, 214, 280, 428, 535, 749, 856, 1070, 1498, 2140, 2996, 3745, 4280, 5992, 7490, 14980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29945 and 29960. The biggest common factor number is the GCF number.
So the greatest common factor 29945 and 29960 is 5.

Also check out the Least Common Multiple of 29945 and 29960