What is the Greatest Common Factor of 290 and 300?

Greatest common factor (GCF) of 290 and 300 is 10.

GCF(290,300) = 10

We will now calculate the prime factors of 290 and 300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 290 and 300.

How to find the GCF of 290 and 300?

We will first find the prime factorization of 290 and 300. After we will calculate the factors of 290 and 300 and find the biggest common factor number .

Step-1: Prime Factorization of 290

Prime factors of 290 are 2, 5, 29. Prime factorization of 290 in exponential form is:

290 = 2¹ × 5¹ × 29¹

Step-2: Prime Factorization of 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

Step-3: Factors of 290

List of positive integer factors of 290 that divides 290 without a remainder.

1, 2, 5, 10, 29, 58, 145

Step-4: Factors of 300

List of positive integer factors of 300 that divides 290 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 290 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 290 and 300 is 10.

Also check out the Least Common Multiple of 290 and 300