What is the Greatest Common Factor of 29736 and 29742?

Greatest common factor (GCF) of 29736 and 29742 is 6.

GCF(29736,29742) = 6

We will now calculate the prime factors of 29736 and 29742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29736 and 29742.

How to find the GCF of 29736 and 29742?

We will first find the prime factorization of 29736 and 29742. After we will calculate the factors of 29736 and 29742 and find the biggest common factor number .

Step-1: Prime Factorization of 29736

Prime factors of 29736 are 2, 3, 7, 59. Prime factorization of 29736 in exponential form is:

29736 = 2³ × 3² × 7¹ × 59¹

Step-2: 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-3: Factors of 29736

List of positive integer factors of 29736 that divides 29736 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 59, 63, 72, 84, 118, 126, 168, 177, 236, 252, 354, 413, 472, 504, 531, 708, 826, 1062, 1239, 1416, 1652, 2124, 2478, 3304, 3717, 4248, 4956, 7434, 9912, 14868

Step-4: Factors of 29742

List of positive integer factors of 29742 that divides 29736 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29736 and 29742. The biggest common factor number is the GCF number.
So the greatest common factor 29736 and 29742 is 6.

Also check out the Least Common Multiple of 29736 and 29742