What is the Greatest Common Factor of 1825 and 1830?

Greatest common factor (GCF) of 1825 and 1830 is 5.

GCF(1825,1830) = 5

We will now calculate the prime factors of 1825 and 1830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1825 and 1830.

How to find the GCF of 1825 and 1830?

We will first find the prime factorization of 1825 and 1830. After we will calculate the factors of 1825 and 1830 and find the biggest common factor number .

Step-1: Prime Factorization of 1825

Prime factors of 1825 are 5, 73. Prime factorization of 1825 in exponential form is:

1825 = 5² × 73¹

Step-2: Prime Factorization of 1830

Prime factors of 1830 are 2, 3, 5, 61. Prime factorization of 1830 in exponential form is:

1830 = 2¹ × 3¹ × 5¹ × 61¹

Step-3: Factors of 1825

List of positive integer factors of 1825 that divides 1825 without a remainder.

1, 5, 25, 73, 365

Step-4: Factors of 1830

List of positive integer factors of 1830 that divides 1825 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1825 and 1830. The biggest common factor number is the GCF number.
So the greatest common factor 1825 and 1830 is 5.

Also check out the Least Common Multiple of 1825 and 1830