What is the Greatest Common Factor of 29400 and 29410?

Greatest common factor (GCF) of 29400 and 29410 is 10.

GCF(29400,29410) = 10

We will now calculate the prime factors of 29400 and 29410, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29400 and 29410.

How to find the GCF of 29400 and 29410?

We will first find the prime factorization of 29400 and 29410. After we will calculate the factors of 29400 and 29410 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 29410

Prime factors of 29410 are 2, 5, 17, 173. Prime factorization of 29410 in exponential form is:

29410 = 2¹ × 5¹ × 17¹ × 173¹

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 29410

List of positive integer factors of 29410 that divides 29400 without a remainder.

1, 2, 5, 10, 17, 34, 85, 170, 173, 346, 865, 1730, 2941, 5882, 14705

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29400 and 29410. The biggest common factor number is the GCF number.
So the greatest common factor 29400 and 29410 is 10.

Also check out the Least Common Multiple of 29400 and 29410