What is the Greatest Common Factor of 29760 and 29780?

Greatest common factor (GCF) of 29760 and 29780 is 20.

GCF(29760,29780) = 20

We will now calculate the prime factors of 29760 and 29780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29760 and 29780.

How to find the GCF of 29760 and 29780?

We will first find the prime factorization of 29760 and 29780. After we will calculate the factors of 29760 and 29780 and find the biggest common factor number .

Step-1: Prime Factorization of 29760

Prime factors of 29760 are 2, 3, 5, 31. Prime factorization of 29760 in exponential form is:

29760 = 2⁶ × 3¹ × 5¹ × 31¹

Step-2: Prime Factorization of 29780

Prime factors of 29780 are 2, 5, 1489. Prime factorization of 29780 in exponential form is:

29780 = 2² × 5¹ × 1489¹

Step-3: Factors of 29760

List of positive integer factors of 29760 that divides 29760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 155, 160, 186, 192, 240, 248, 310, 320, 372, 465, 480, 496, 620, 744, 930, 960, 992, 1240, 1488, 1860, 1984, 2480, 2976, 3720, 4960, 5952, 7440, 9920, 14880

Step-4: Factors of 29780

List of positive integer factors of 29780 that divides 29760 without a remainder.

1, 2, 4, 5, 10, 20, 1489, 2978, 5956, 7445, 14890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29760 and 29780. The biggest common factor number is the GCF number.
So the greatest common factor 29760 and 29780 is 20.

Also check out the Least Common Multiple of 29760 and 29780