What Is the GCF of 55 & 100?

Greatest Common Factor

• The greatest common factor (GCF) between two numbers is the largest factor that will divide into both numbers. Finding the GCF is useful when simplifying large fractions by finding the greatest common multiple that will divide into both the numerator and the denominator. That factor is divided out and the result is the simplified fraction.

Prime Factorizations: 55 &100

• The prime number multiples of a number can be found through some trial and error. For example, it is easy to see that 55 = 5 * 11. Because these are both prime numbers, the prime factorization of 55 is complete at 5 and 11.

  The prime factorization of 100 could begin with 100 / 5 = 20. Keep breaking down the result until it is in only prime numbers. 20 / 5 = 4; 4 / 2 = 2. So the prime factorization of 100 is 2, 2, 5 and 5. Note that it is important to write out every occurrence of each factor.

GCF: 55 &100

• To find the greatest common factor of two numbers, multiply the factors that they have in common. For 55 and 100, the only factor they have in common is 5 so no multiplication needs to take place. The GCF simply equals 5.

Used in Example

• To see why this process might come in handy, add the fractions 25/100 + 30/100. Add the numerators while maintaining the denominator: 55/100. Simplify the fraction by dividing out the greatest common factor, which has been identified as 5: (55/5) / (100/5) = 11 / 20. That is the simplest form of the fraction possible.