What is the Greatest Common Factor of 29386 and 29400?

Greatest common factor (GCF) of 29386 and 29400 is 14.

GCF(29386,29400) = 14

We will now calculate the prime factors of 29386 and 29400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29386 and 29400.

How to find the GCF of 29386 and 29400?

We will first find the prime factorization of 29386 and 29400. After we will calculate the factors of 29386 and 29400 and find the biggest common factor number .

Step-1: Prime Factorization of 29386

Prime factors of 29386 are 2, 7, 2099. Prime factorization of 29386 in exponential form is:

29386 = 2¹ × 7¹ × 2099¹

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 29386

List of positive integer factors of 29386 that divides 29386 without a remainder.

1, 2, 7, 14, 2099, 4198, 14693

Step-4: Factors of 29400

List of positive integer factors of 29400 that divides 29386 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 29386 and 29400. The biggest common factor number is the GCF number.
So the greatest common factor 29386 and 29400 is 14.

Also check out the Least Common Multiple of 29386 and 29400