What is the Greatest Common Factor of 29385 and 29400?

Greatest common factor (GCF) of 29385 and 29400 is 15.

GCF(29385,29400) = 15

We will now calculate the prime factors of 29385 and 29400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29385 and 29400.

How to find the GCF of 29385 and 29400?

We will first find the prime factorization of 29385 and 29400. After we will calculate the factors of 29385 and 29400 and find the biggest common factor number .

Step-1: Prime Factorization of 29385

Prime factors of 29385 are 3, 5, 653. Prime factorization of 29385 in exponential form is:

29385 = 3² × 5¹ × 653¹

Step-2: Prime Factorization of 29400

Prime factors of 29400 are 2, 3, 5, 7. Prime factorization of 29400 in exponential form is:

29400 = 2³ × 3¹ × 5² × 7²

Step-3: Factors of 29385

List of positive integer factors of 29385 that divides 29385 without a remainder.

1, 3, 5, 9, 15, 45, 653, 1959, 3265, 5877, 9795

Step-4: Factors of 29400

List of positive integer factors of 29400 that divides 29385 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 49, 50, 56, 60, 70, 75, 84, 98, 100, 105, 120, 140, 147, 150, 168, 175, 196, 200, 210, 245, 280, 294, 300, 350, 392, 420, 490, 525, 588, 600, 700, 735, 840, 980, 1050, 1176, 1225, 1400, 1470, 1960, 2100, 2450, 2940, 3675, 4200, 4900, 5880, 7350, 9800, 14700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29385 and 29400. The biggest common factor number is the GCF number.
So the greatest common factor 29385 and 29400 is 15.

Also check out the Least Common Multiple of 29385 and 29400