What is the Greatest Common Factor of 10074 and 10090?

Greatest common factor (GCF) of 10074 and 10090 is 2.

GCF(10074,10090) = 2

We will now calculate the prime factors of 10074 and 10090, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10074 and 10090.

How to find the GCF of 10074 and 10090?

We will first find the prime factorization of 10074 and 10090. After we will calculate the factors of 10074 and 10090 and find the biggest common factor number .

Step-1: Prime Factorization of 10074

Prime factors of 10074 are 2, 3, 23, 73. Prime factorization of 10074 in exponential form is:

10074 = 2¹ × 3¹ × 23¹ × 73¹

Step-2: Prime Factorization of 10090

Prime factors of 10090 are 2, 5, 1009. Prime factorization of 10090 in exponential form is:

10090 = 2¹ × 5¹ × 1009¹

Step-3: Factors of 10074

List of positive integer factors of 10074 that divides 10074 without a remainder.

1, 2, 3, 6, 23, 46, 69, 73, 138, 146, 219, 438, 1679, 3358, 5037

Step-4: Factors of 10090

List of positive integer factors of 10090 that divides 10074 without a remainder.

1, 2, 5, 10, 1009, 2018, 5045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10074 and 10090. The biggest common factor number is the GCF number.
So the greatest common factor 10074 and 10090 is 2.

Also check out the Least Common Multiple of 10074 and 10090