Greatest Common Factor (GCF) and Distributive Property
Use the GCF and the Distributive Property to express the sum as a product.
15 + 35
5( 3 + 7 ) or 5 x ( 3 + 7 )
Which pair of numbers has a least common multiple of 24?
A. 2 and 8
B. 6 and 8
C. 9 and 12
D. 3 and 18
B. 6 and 8
What is the prime factorization of 48?
2 x 2 x 2 x 2 x 3 or 24 x 3
What is the prime factorization of 39?
3 x 13
Areli has two planks of plywood to make shelves. One of the planks is 4 2/3 feet long and the other plank is 5 1/6 long. How much plywood does she have to make the shelves?
4 2/3 + 5 1/6 = 4 4/6 + 5 1/6
9 5/6 feet of plywood total.
Use the GCF and the Distributive Property to express the sum as a product.
18 + 24
6(3+4) or 6 x ( 3 + 4 )
What is the least common multiple of 2, 3, and 5?
30
What is the prime factorization of 70?
2 x 5 x 7
How many prime factors does the prime factorization of 1000 have?
6 prime factors: 2 x 2 x 2 x 5 x 5 x 5 or 23 x 53
You have 42 red cards and 63 blue cards. You are putting them into sets.
Each set has the same amount of red cards and each set has the same amount of blue cards.
How many sets can you make?
Challenge: How many red cards are in each set and how many blue cards are in each set?
You can make 7 sets.
Challenge: Each set has 6 red cards and 9 blue cards.
Use the GCF and the Distributive Property to express the sum as a product.
36 + 48
12(3 + 4) or 12 x ( 3 + 4)
What is the least common multiple of 20 and 12?
60
What is the prime factorization of 90?
2 x 3 x 3 x 5 or 2 x 32 x 5
How many prime factors does the prime factorization of 512 have?
9 prime factors: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 or 29
Joanna bought cookies and cupcakes for a party. The cookies are sold in packs of 10 and the cupcakes are sold in packs of 12. Joanna bought as few packs as possible to have the same number of cookies and cupcakes.
How many total cupcakes did she buy?
Challenge: How many packs of cookies and cupcakes did she buy?
She bought 60 cupcakes.
Challenge: She bought 6 packs of cookies and 5 packs of cupcakes.
Use the GCF and the Distributive Property to express the sum as a product.
81 + 108
9(9 + 12) or 9 x ( 9 + 12 )
What is the least common multiple of 4, 8, and 10?
40
What is the prime factorization of 99?
3 x 3 x 11 or 32 x 11
What is the prime factorization of 630?
2 x 3 x 3 x 5 x 7 or 2 x 32 x 5 x 7
There are 84 boys and 72 girls going on a field trip.
The students are split into groups. Each group has an equal number of boys in it and an equal number of girls in it.
How many groups will the students be split into?
Challenge: How many boys and girls will be in each group?
The students are broken into 12 groups.
Challenge: There are 7 boys and 6 girls in each group.
Use the GCF and the Distributive Property to express the sum as a product.
100 + 75
25(4 + 3) or 25 x ( 4 + 3 )
What is the least common multiple of 12, 15, and 20?
60
What is the prime factorization of 280?
2 x 2 x 2 x 5 x 7 or 23 x 5 x 7
What is the prime factorization of 770?
2 x 5 x 7 x 11
Damari had 4 1/6 lbs of apples. He made an apple turnover with 1 3/4 lbs of the apples. How many pounds of apples does he have left to make an apple pie?
4 1/6 - 1 3/4 = 4 2/12 - 1 9/12
You have to borrow 1 whole or 12/12 from the 4.
3 14/12 - 1 9/12
2 5/12 lbs of apples left to make apple pie.