What is the Greatest Common Factor of 29400 and 29408?

Greatest common factor (GCF) of 29400 and 29408 is 8.

GCF(29400,29408) = 8

We will now calculate the prime factors of 29400 and 29408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29400 and 29408.

How to find the GCF of 29400 and 29408?

We will first find the prime factorization of 29400 and 29408. After we will calculate the factors of 29400 and 29408 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29408

Prime factors of 29408 are 2, 919. Prime factorization of 29408 in exponential form is:

29408 = 2⁵ × 919¹

Step-3: Factors of 29400

List of positive integer factors of 29400 that divides 29400 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

Step-4: Factors of 29408

List of positive integer factors of 29408 that divides 29400 without a remainder.

1, 2, 4, 8, 16, 32, 919, 1838, 3676, 7352, 14704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29400 and 29408. The biggest common factor number is the GCF number.
So the greatest common factor 29400 and 29408 is 8.

Also check out the Least Common Multiple of 29400 and 29408