What is the Greatest Common Factor of 29742 and 29760?

Greatest common factor (GCF) of 29742 and 29760 is 6.

GCF(29742,29760) = 6

We will now calculate the prime factors of 29742 and 29760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29742 and 29760.

How to find the GCF of 29742 and 29760?

We will first find the prime factorization of 29742 and 29760. After we will calculate the factors of 29742 and 29760 and find the biggest common factor number .

Step-1: Prime Factorization of 29742

Prime factors of 29742 are 2, 3, 4957. Prime factorization of 29742 in exponential form is:

29742 = 2¹ × 3¹ × 4957¹

Step-2: 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-3: Factors of 29742

List of positive integer factors of 29742 that divides 29742 without a remainder.

1, 2, 3, 6, 4957, 9914, 14871

Step-4: Factors of 29760

List of positive integer factors of 29760 that divides 29742 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29742 and 29760. The biggest common factor number is the GCF number.
So the greatest common factor 29742 and 29760 is 6.

Also check out the Least Common Multiple of 29742 and 29760