Lesson 4.2Greatest Common Factor

Essential Question: How do you find the greatest common factor (GCF) of two or more numbers?

Before we start…

What does it mean to have something in common?

What do the numbers 6 and 10 have in common?

What is a factor?

Any whole number that can be divided evenly into another number

1, 2, 3, and 6 are factors of 6

What is a common factor?

A whole number that is a factor of two or more nonzero whole numbers

3 is a common factor of 3, 6, 9 and 12.

What is the greatest common factor (GCF)?

The greatest of the common factors.

– It’s the highest number factor that appears in each number’s factor list.

12 has the factors: 1, 2, 3, 4, 6 and 12.

16 has the factors: 1, 2, 4, 8 and 16.

– The GCF of 12 and 16 would be 4.

How do you find a GCF?

• Write the prime factorization of each number.

• Find the common prime factors.

• Multiply the factors. Your product is the GCF.

Find the greatest common factor of 12 and 30.

Find the greatest common factor of 21 and 42.

Find the greatest common factor of 42 and 60.

Find the greatest common factor of 36 and 90.

Find the greatest common factor of 3, 9 and 27.

Find the greatest common factor of 21, 28 and 56.

What if there isn’t any GCF?

• Sometimes you’ll have numbers that won’t have any factor in common other than 1.

• Two numbers are relatively prime if their greatest common factor is 1.– 8 and 15 are relatively prime.

Tell whether the numbers 24 and 45 are relatively prime.

Tell whether the numbers 9 and 20 are relatively prime.

Tell whether the numbers 10 and 25 are relatively prime.

Tell whether the numbers 35 and 54 are relatively prime.

Music Choir A choir director wants to divide a choir into smaller groups. The choir has 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice. What is the greatest number of groups that can be formed? How many sopranos, altos, and tenors will be in each group?

Pep Rally Students at your school are planning to hand out pep rally packs to support your school’s athletic program. The students have 240 bumper stickers, 360 pennants, and 720 pencils. Every pack must have the same contents, and no items should be left over. What is the greatest number of packs that can be made? What will each pack contain?

Snacks Elisha and David are putting together snack packs for a large group of hikers. They have 160 apples, 320 carrot sticks, and 400 celery sticks. Each snack pack has the same contents and there are no leftover items. What is the greatest number of snack packs that can be made and what is in each pack?

Soccer Teams In a youth sports league, 50 girls and 60 boys will be divided into teams. Each team will have an equal number of players and will have the same number of girls. What is the greatest number of teams that can be formed? How many boys and girls are on each team?

What about the GCF of monomials?

• You can find the greatest common factor of two monomials by factoring the monomials and taking their common factors.

Find the greatest common factor of and .

Find the greatest common factor of and .

Find the greatest common factor of and .

Find the greatest common factor of and .

Find the greatest common factor of and .

Find the greatest common factor of and .

How do you find the greatest common factor (GCF) of two or more numbers?

Ticket Out the Door

Find the greatest common factor of 18 and 33.