Greatest Common Factor (GCF)

Honors Math – Grade 7

Problem of the DayMary has 45 feet of rope, and Peter has 60 feet. What is the longest length they can cut from each rope so that all the pieces are equal in length?

To find the longest length of cut rope, find the greatest common factor (GCF) of 45 and 60.

The Greatest Common Factor (GCF) of two or more numbers, is the largest number that is a factor of these numbers.

VOCABULARY ALERT

The Prime Factorization of a number can be used to find the GCF of two or more numbers.

Prime Number – a number that has exactly two factors: itself and 1.Composite Number – a number that has many factors.

VOCABULARY ALERT

To use the prime factorization to find the GCF:1. Make a factor tree for each number.2. Identify common prime factors.3. Multiply common prime factors.

Using Factor Trees to find the GCF.

Mary and Peter can cut, at most, 15-ft lengths from each rope.

Find the GCF of each set of numbers.

18 and 24

32 and 96

81 and 54

Using Factor Trees to find the GCF.

The GCF is used to simplify fractions. A fraction is insimplest form (lowest terms) if the GCF of its numeratorand denominator is 1.

42

14Simplify

66

44Simplify

To write an equivalent fraction, multiply or divide BOTH numerator and denominator by the same nonzero number.

Write two equivalent fractions for each fraction.

144

81

96

72

9

4

Find the value of n that makes the fractions equivalent.

568

5 n

460

45 n

279

4 n

n

3

96

72

To change a decimal to a fraction…1. Write all the digits after the decimal point as the

numerator.2. Use the place value of the farthest digit to the right as

the denominator.3. Write in simplest form.

35.0

What is the place?

008.6

What is the place?

Write as a fraction in simplest form.

55.0

36.1

06.2