How does finding the GCF help you to solve real-world problems?

Answer 1

Example: 30/42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Divide the numerator and the denominator by the GCF.

30/6 = 5

42/6 = 7

30/42 = 5/7

Answer 2

Finding the GCF helps to reduce fractions to their lowest terms.

Finding the LCM helps to add and subtract fractions with different denominators by finding their lowest common denominator.

Answer 3

If you have an answer that is a fraction, finding the GCF of the numerator and denominator can help you simplify your answer. Divide the top and bottom by the GCF to write the fraction in simplest form.

Answer 4

The GCF of 4 and 5 is 201/4 + 2/5 = 5/20 + 8/20 = 13/20.
An extremely simplistic real-world example: If you spend a quarter of your net income on rent and utilities, and two fifths on food and clothing, what proportion of your income is gone before you can think even about spending on "fun" things?

Answer 5

You are left to work with smaller numbers.

Answer 6

Example: 30 and 42

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Answer 7

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF

Answer 8

Once you have found the GCF of the numerator and denominator of a fraction, divide both by the GCF.