What is the Greatest Common Factor of 30419 and 30438?

Greatest common factor (GCF) of 30419 and 30438 is 19.

GCF(30419,30438) = 19

We will now calculate the prime factors of 30419 and 30438, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30419 and 30438.

How to find the GCF of 30419 and 30438?

We will first find the prime factorization of 30419 and 30438. After we will calculate the factors of 30419 and 30438 and find the biggest common factor number .

Step-1: Prime Factorization of 30419

Prime factors of 30419 are 19, 1601. Prime factorization of 30419 in exponential form is:

30419 = 19¹ × 1601¹

Step-2: Prime Factorization of 30438

Prime factors of 30438 are 2, 3, 19, 89. Prime factorization of 30438 in exponential form is:

30438 = 2¹ × 3² × 19¹ × 89¹

Step-3: Factors of 30419

List of positive integer factors of 30419 that divides 30419 without a remainder.

1, 19, 1601

Step-4: Factors of 30438

List of positive integer factors of 30438 that divides 30419 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 89, 114, 171, 178, 267, 342, 534, 801, 1602, 1691, 3382, 5073, 10146, 15219

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30419 and 30438. The biggest common factor number is the GCF number.
So the greatest common factor 30419 and 30438 is 19.

Also check out the Least Common Multiple of 30419 and 30438