What is the Greatest Common Factor of 30640 and 30654?

Greatest common factor (GCF) of 30640 and 30654 is 2.

GCF(30640,30654) = 2

We will now calculate the prime factors of 30640 and 30654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30640 and 30654.

How to find the GCF of 30640 and 30654?

We will first find the prime factorization of 30640 and 30654. After we will calculate the factors of 30640 and 30654 and find the biggest common factor number .

Step-1: Prime Factorization of 30640

Prime factors of 30640 are 2, 5, 383. Prime factorization of 30640 in exponential form is:

30640 = 2⁴ × 5¹ × 383¹

Step-2: Prime Factorization of 30654

Prime factors of 30654 are 2, 3, 13, 131. Prime factorization of 30654 in exponential form is:

30654 = 2¹ × 3² × 13¹ × 131¹

Step-3: Factors of 30640

List of positive integer factors of 30640 that divides 30640 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 383, 766, 1532, 1915, 3064, 3830, 6128, 7660, 15320

Step-4: Factors of 30654

List of positive integer factors of 30654 that divides 30640 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 131, 234, 262, 393, 786, 1179, 1703, 2358, 3406, 5109, 10218, 15327

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30640 and 30654. The biggest common factor number is the GCF number.
So the greatest common factor 30640 and 30654 is 2.

Also check out the Least Common Multiple of 30640 and 30654