What is the Greatest Common Factor of 29760 and 29778?

Greatest common factor (GCF) of 29760 and 29778 is 6.

GCF(29760,29778) = 6

We will now calculate the prime factors of 29760 and 29778, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29760 and 29778.

How to find the GCF of 29760 and 29778?

We will first find the prime factorization of 29760 and 29778. After we will calculate the factors of 29760 and 29778 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 29778

Prime factors of 29778 are 2, 3, 7, 709. Prime factorization of 29778 in exponential form is:

29778 = 2¹ × 3¹ × 7¹ × 709¹

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 29778

List of positive integer factors of 29778 that divides 29760 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 709, 1418, 2127, 4254, 4963, 9926, 14889

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29760 and 29778. The biggest common factor number is the GCF number.
So the greatest common factor 29760 and 29778 is 6.

Also check out the Least Common Multiple of 29760 and 29778