What is the Greatest Common Factor of 9 and 100?

Greatest common factor (GCF) of 9 and 100 is 1.

GCF(9,100) = 1

We will now calculate the prime factors of 9 and 100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9 and 100.

How to find the GCF of 9 and 100?

We will first find the prime factorization of 9 and 100. After we will calculate the factors of 9 and 100 and find the biggest common factor number .

Step-1: Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 3²

Step-2: Prime Factorization of 100

Prime factors of 100 are 2, 5. Prime factorization of 100 in exponential form is:

100 = 2² × 5²

Step-3: Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3

Step-4: Factors of 100

List of positive integer factors of 100 that divides 9 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9 and 100. The biggest common factor number is the GCF number.
So the greatest common factor 9 and 100 is 1.

Also check out the Least Common Multiple of 9 and 100