Greatest Common Factor & Word Problems

Greatest Common Factor Definition: 
Greatest common factor, in short GCF is the highest of the common factors of two or more numbers

Greatest Common Factor

For example:
Find the GCF of 12, 24 and 18
Solution: First we find the factors of,
12 = 1,2,3,4,6,12
24 = 1,2,3,4,6,8,12,24
18 = 1,2,3,6,9,18
From the above list of factors, we can see that 6 is the highest common factor
 So, the GCF of the number 12, 24 and 18 is 6

Let us solve some Greatest common factor word problems (GCF word problems):
1. Edina has 72 inches and 90 inches wide cloth strips. How wide should she cut them into strips of equal width that are as wide as possible?
Solution: To find the greatest possible width, we need to find the common factors of 72 and 90
Factors of,
72 = 1,2,3,4,6,8,9,12,18,24,36 and 72
90 = 1,2,3,4,5,6,9,10,15,18,30,45 and 90
Common factors are 1, 2, 3, 4, 6,9,18
Highest common factor is 18
Edina needs to cut each strip 18 inches wide

2. Wilma is making flower arrangements. She has 8 roses and 16 daisies. If she wants to make arrangements identical with no flower left over, what is the greatest number of arrangements possible?
Solution: Factors of 8 and 16 are
8 = 2 x 2 x 2
16 = 2 x 2 x 2 x 2
Common factors are 2, 2, and 2
Since 2 is repeating thrice, the GCF will be product of them, 2 x 2 x 2 = 8
Wilma can make 8 arrangements

GCF learning (GCF learn free):
GCF is Greatest Common Factor, which is the highest of the common factors of the given numbers.
Common Factors are factors which are common to the list of factors of the given numbers
Example: Find the GCF of 12 and 16
Solution: factors of 12 are 1, 2, 3, 4, 6 and 12
 Factors of 16 are 1, 2, 4, 8 and 16
  common factors are 1, 2 and 4
GCF of 12 and 16 will be 4, it being the highest common factor