What is the Greatest Common Factor of 29745 and 29754?

Greatest common factor (GCF) of 29745 and 29754 is 9.

GCF(29745,29754) = 9

We will now calculate the prime factors of 29745 and 29754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29745 and 29754.

How to find the GCF of 29745 and 29754?

We will first find the prime factorization of 29745 and 29754. After we will calculate the factors of 29745 and 29754 and find the biggest common factor number .

Step-1: Prime Factorization of 29745

Prime factors of 29745 are 3, 5, 661. Prime factorization of 29745 in exponential form is:

29745 = 3² × 5¹ × 661¹

Step-2: 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-3: Factors of 29745

List of positive integer factors of 29745 that divides 29745 without a remainder.

1, 3, 5, 9, 15, 45, 661, 1983, 3305, 5949, 9915

Step-4: Factors of 29754

List of positive integer factors of 29754 that divides 29745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29745 and 29754. The biggest common factor number is the GCF number.
So the greatest common factor 29745 and 29754 is 9.

Also check out the Least Common Multiple of 29745 and 29754