What is the Greatest Common Factor of 29745 and 29750?

Greatest common factor (GCF) of 29745 and 29750 is 5.

GCF(29745,29750) = 5

We will now calculate the prime factors of 29745 and 29750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29745 and 29750.

How to find the GCF of 29745 and 29750?

We will first find the prime factorization of 29745 and 29750. After we will calculate the factors of 29745 and 29750 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 29750

Prime factors of 29750 are 2, 5, 7, 17. Prime factorization of 29750 in exponential form is:

29750 = 2¹ × 5³ × 7¹ × 17¹

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 29750

List of positive integer factors of 29750 that divides 29745 without a remainder.

1, 2, 5, 7, 10, 14, 17, 25, 34, 35, 50, 70, 85, 119, 125, 170, 175, 238, 250, 350, 425, 595, 850, 875, 1190, 1750, 2125, 2975, 4250, 5950, 14875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29745 and 29750. The biggest common factor number is the GCF number.
So the greatest common factor 29745 and 29750 is 5.

Also check out the Least Common Multiple of 29745 and 29750