What is the Greatest Common Factor of 30140 and 30160?

Greatest common factor (GCF) of 30140 and 30160 is 20.

GCF(30140,30160) = 20

We will now calculate the prime factors of 30140 and 30160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30140 and 30160.

How to find the GCF of 30140 and 30160?

We will first find the prime factorization of 30140 and 30160. After we will calculate the factors of 30140 and 30160 and find the biggest common factor number .

Step-1: Prime Factorization of 30140

Prime factors of 30140 are 2, 5, 11, 137. Prime factorization of 30140 in exponential form is:

30140 = 2² × 5¹ × 11¹ × 137¹

Step-2: Prime Factorization of 30160

Prime factors of 30160 are 2, 5, 13, 29. Prime factorization of 30160 in exponential form is:

30160 = 2⁴ × 5¹ × 13¹ × 29¹

Step-3: Factors of 30140

List of positive integer factors of 30140 that divides 30140 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 137, 220, 274, 548, 685, 1370, 1507, 2740, 3014, 6028, 7535, 15070

Step-4: Factors of 30160

List of positive integer factors of 30160 that divides 30140 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 29, 40, 52, 58, 65, 80, 104, 116, 130, 145, 208, 232, 260, 290, 377, 464, 520, 580, 754, 1040, 1160, 1508, 1885, 2320, 3016, 3770, 6032, 7540, 15080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30140 and 30160. The biggest common factor number is the GCF number.
So the greatest common factor 30140 and 30160 is 20.

Also check out the Least Common Multiple of 30140 and 30160