What is the Greatest Common Factor of 29754 and 29772?

Greatest common factor (GCF) of 29754 and 29772 is 18.

GCF(29754,29772) = 18

We will now calculate the prime factors of 29754 and 29772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29754 and 29772.

How to find the GCF of 29754 and 29772?

We will first find the prime factorization of 29754 and 29772. After we will calculate the factors of 29754 and 29772 and find the biggest common factor number .

Step-1: Prime Factorization of 29754

Prime factors of 29754 are 2, 3, 19, 29. Prime factorization of 29754 in exponential form is:

29754 = 2¹ × 3³ × 19¹ × 29¹

Step-2: Prime Factorization of 29772

Prime factors of 29772 are 2, 3, 827. Prime factorization of 29772 in exponential form is:

29772 = 2² × 3² × 827¹

Step-3: Factors of 29754

List of positive integer factors of 29754 that divides 29754 without a remainder.

1, 2, 3, 6, 9, 18, 19, 27, 29, 38, 54, 57, 58, 87, 114, 171, 174, 261, 342, 513, 522, 551, 783, 1026, 1102, 1566, 1653, 3306, 4959, 9918, 14877

Step-4: Factors of 29772

List of positive integer factors of 29772 that divides 29754 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 827, 1654, 2481, 3308, 4962, 7443, 9924, 14886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29754 and 29772. The biggest common factor number is the GCF number.
So the greatest common factor 29754 and 29772 is 18.

Also check out the Least Common Multiple of 29754 and 29772