What is the Greatest Common Factor of 37825 and 37842?

Greatest common factor (GCF) of 37825 and 37842 is 17.

GCF(37825,37842) = 17

We will now calculate the prime factors of 37825 and 37842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37825 and 37842.

How to find the GCF of 37825 and 37842?

We will first find the prime factorization of 37825 and 37842. After we will calculate the factors of 37825 and 37842 and find the biggest common factor number .

Step-1: Prime Factorization of 37825

Prime factors of 37825 are 5, 17, 89. Prime factorization of 37825 in exponential form is:

37825 = 5² × 17¹ × 89¹

Step-2: Prime Factorization of 37842

Prime factors of 37842 are 2, 3, 7, 17, 53. Prime factorization of 37842 in exponential form is:

37842 = 2¹ × 3¹ × 7¹ × 17¹ × 53¹

Step-3: Factors of 37825

List of positive integer factors of 37825 that divides 37825 without a remainder.

1, 5, 17, 25, 85, 89, 425, 445, 1513, 2225, 7565

Step-4: Factors of 37842

List of positive integer factors of 37842 that divides 37825 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 53, 102, 106, 119, 159, 238, 318, 357, 371, 714, 742, 901, 1113, 1802, 2226, 2703, 5406, 6307, 12614, 18921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37825 and 37842. The biggest common factor number is the GCF number.
So the greatest common factor 37825 and 37842 is 17.

Also check out the Least Common Multiple of 37825 and 37842