What is the GCF and LCM of 25 and 55?

The Greatest Common Factor (GCF) of 25 and 55 is 5, and the Least Common Multiple (LCM) is 275.

Understanding GCF and LCM

Here's a breakdown of how to determine the GCF and LCM:

• GCF (Greatest Common Factor): The largest number that divides evenly into both 25 and 55.
• LCM (Least Common Multiple): The smallest number that is a multiple of both 25 and 55.

Calculating the GCF and LCM

Here's one method for finding the GCF and LCM:

1. Prime Factorization:
   • 25 = 5 x 5 = 5²
   • 55 = 5 x 11
2. GCF: Identify the common prime factors and their lowest powers.
   • The only common prime factor is 5, and its lowest power is 5¹ = 5.
   • Therefore, GCF(25, 55) = 5.
3. LCM: Identify all prime factors and their highest powers present in either number.
   • Prime factors are 5 and 11. The highest power of 5 is 5², and the highest power of 11 is 11¹.
   • Therefore, LCM(25, 55) = 5² x 11 = 25 x 11 = 275.

Summary

Number	Prime Factorization
25	5 x 5
55	5 x 11
GCF	5
LCM	275

As stated in the reference, if the LCM of 25 and 55 is 275, then the GCF of 25 and 55 is 5. Conversely, if the GCF is 5 and the LCM is 275, we are dealing with the numbers 25 and 55.