What is the Greatest Common Factor of 29760 and 29768?

Greatest common factor (GCF) of 29760 and 29768 is 8.

GCF(29760,29768) = 8

We will now calculate the prime factors of 29760 and 29768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29760 and 29768.

How to find the GCF of 29760 and 29768?

We will first find the prime factorization of 29760 and 29768. After we will calculate the factors of 29760 and 29768 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 29768

Prime factors of 29768 are 2, 61. Prime factorization of 29768 in exponential form is:

29768 = 2³ × 61²

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 29768

List of positive integer factors of 29768 that divides 29760 without a remainder.

1, 2, 4, 8, 61, 122, 244, 488, 3721, 7442, 14884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29760 and 29768. The biggest common factor number is the GCF number.
So the greatest common factor 29760 and 29768 is 8.

Also check out the Least Common Multiple of 29760 and 29768