What is the Greatest Common Factor of 40 and 200?

Greatest common factor (GCF) of 40 and 200 is 40.

GCF(40,200) = 40

We will now calculate the prime factors of 40 and 200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40 and 200.

How to find the GCF of 40 and 200?

We will first find the prime factorization of 40 and 200. After we will calculate the factors of 40 and 200 and find the biggest common factor number .

Step-1: Prime Factorization of 40

Prime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:

40 = 2³ × 5¹

Step-2: Prime Factorization of 200

Prime factors of 200 are 2, 5. Prime factorization of 200 in exponential form is:

200 = 2³ × 5²

Step-3: Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20

Step-4: Factors of 200

List of positive integer factors of 200 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 40 and 200. The biggest common factor number is the GCF number.
So the greatest common factor 40 and 200 is 40.

Also check out the Least Common Multiple of 40 and 200