What is the Greatest Common Factor of 49290 and 49300?

Greatest common factor (GCF) of 49290 and 49300 is 10.

GCF(49290,49300) = 10

We will now calculate the prime factors of 49290 and 49300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49290 and 49300.

How to find the GCF of 49290 and 49300?

We will first find the prime factorization of 49290 and 49300. After we will calculate the factors of 49290 and 49300 and find the biggest common factor number .

Step-1: Prime Factorization of 49290

Prime factors of 49290 are 2, 3, 5, 31, 53. Prime factorization of 49290 in exponential form is:

49290 = 2¹ × 3¹ × 5¹ × 31¹ × 53¹

Step-2: Prime Factorization of 49300

Prime factors of 49300 are 2, 5, 17, 29. Prime factorization of 49300 in exponential form is:

49300 = 2² × 5² × 17¹ × 29¹

Step-3: Factors of 49290

List of positive integer factors of 49290 that divides 49290 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 31, 53, 62, 93, 106, 155, 159, 186, 265, 310, 318, 465, 530, 795, 930, 1590, 1643, 3286, 4929, 8215, 9858, 16430, 24645

Step-4: Factors of 49300

List of positive integer factors of 49300 that divides 49290 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 29, 34, 50, 58, 68, 85, 100, 116, 145, 170, 290, 340, 425, 493, 580, 725, 850, 986, 1450, 1700, 1972, 2465, 2900, 4930, 9860, 12325, 24650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49290 and 49300. The biggest common factor number is the GCF number.
So the greatest common factor 49290 and 49300 is 10.

Also check out the Least Common Multiple of 49290 and 49300