What is the Greatest Common Factor of 35400 and 35408?

Greatest common factor (GCF) of 35400 and 35408 is 8.

GCF(35400,35408) = 8

We will now calculate the prime factors of 35400 and 35408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35400 and 35408.

How to find the GCF of 35400 and 35408?

We will first find the prime factorization of 35400 and 35408. After we will calculate the factors of 35400 and 35408 and find the biggest common factor number .

Step-1: Prime Factorization of 35400

Prime factors of 35400 are 2, 3, 5, 59. Prime factorization of 35400 in exponential form is:

35400 = 2³ × 3¹ × 5² × 59¹

Step-2: Prime Factorization of 35408

Prime factors of 35408 are 2, 2213. Prime factorization of 35408 in exponential form is:

35408 = 2⁴ × 2213¹

Step-3: Factors of 35400

List of positive integer factors of 35400 that divides 35400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 59, 60, 75, 100, 118, 120, 150, 177, 200, 236, 295, 300, 354, 472, 590, 600, 708, 885, 1180, 1416, 1475, 1770, 2360, 2950, 3540, 4425, 5900, 7080, 8850, 11800, 17700

Step-4: Factors of 35408

List of positive integer factors of 35408 that divides 35400 without a remainder.

1, 2, 4, 8, 16, 2213, 4426, 8852, 17704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35400 and 35408. The biggest common factor number is the GCF number.
So the greatest common factor 35400 and 35408 is 8.

Also check out the Least Common Multiple of 35400 and 35408