What is the Greatest Common Factor of 29760 and 29766?

Greatest common factor (GCF) of 29760 and 29766 is 6.

GCF(29760,29766) = 6

We will now calculate the prime factors of 29760 and 29766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29760 and 29766.

How to find the GCF of 29760 and 29766?

We will first find the prime factorization of 29760 and 29766. After we will calculate the factors of 29760 and 29766 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 29766

Prime factors of 29766 are 2, 3, 11, 41. Prime factorization of 29766 in exponential form is:

29766 = 2¹ × 3¹ × 11² × 41¹

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 29766

List of positive integer factors of 29766 that divides 29760 without a remainder.

1, 2, 3, 6, 11, 22, 33, 41, 66, 82, 121, 123, 242, 246, 363, 451, 726, 902, 1353, 2706, 4961, 9922, 14883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29760 and 29766. The biggest common factor number is the GCF number.
So the greatest common factor 29760 and 29766 is 6.

Also check out the Least Common Multiple of 29760 and 29766