This document provides a lesson on factor trees, prime factorization, greatest common factors (GCF), and using the distributive property to write sums as products. It includes examples and practice problems for students to work through. For factor trees and prime factorization, students find the prime factors of numbers like 36, 28, 45, and 72. For GCF, they use factor trees to find the GCF of pairs of numbers and complete Venn diagrams. Finally, for the distributive property, students write sums as products where the GCF is a factor and the remaining numbers form the sum, such as 24 + 16 = 4(6 + 4). The document ends with homework practice applying these concepts.

1. Name _________________________________________
Mrs. Labuski / Mrs. Portsmore Period ______
Date __________________
Fifth Grade Flashback!!
Concept 1: Factor Trees & Prime Factorization
To find the Prime Factorization of each number use a Factor Tree
36
1. Choose any two factors of the number:
3 12
2. Circle the prime number
2 6
3. Keep finding factors until each branch ends in a prime number
2 3
4. Rewrite the factors in order
36= 3 2 2 3
5. Combine any factors into exponential form
36= 22 32
Now let’s try one together:
1.
28
What divisibility rule
can help you? ____
2.
____________________
3.
50
What divisibility rule
can help you? ____
____________________
45
What divisibility rule
can help you? ____
____________________
4.
72
What divisibility rule
can help you? ____
____________________

2. Concept 2 Greatest Common Factor
Use Factor Trees to help you find the Greatest Common Factor of two numbers.
Draw your factor trees
Complete the Venn Diagram.
Multiply the common factors to find the GCF
GCF
GCF
GCF: 2 x 5 = 10
GCF= 10
GCF: 3 x 5 = 10
GCF = 15
Now you try:
1- factor trees
2 – Venn diagrams
GCF
GCF

3. Concept 3 GCF & Distributive
Example: 36 + 8 as 4(9 + 2).
Step 1: Find the GCF of the numbers in the sum. GCF of 36 and 8 is 4.
Step 2: Replace each number by a product of the GCF and its other factor.
36 + 8 = 4 9 + 4 2
Step 3: Replace the sum of the products by two factors with the GCF as a multiple of the sum of
two whole numbers.
36 + 8 = 4 9 + 4 2 = 4(9 + 2)
Write each of the following sums as two factors of their GCF and a sum:
1) 24 + 16 (GCF=_4____)
___4(6+4)_____
4) 63 + 54 (GCF=_____)
______________
7) 54 + 36 (GCF=_____)
______________
10) 20 + 44
______________
2) 25 + 15 (GCF=_____)
_______________
5) 80 + 30 (GCF=_____)
_______________
8) 49 + 84 (GCF=_____)
_______________
11) 4 + 12
_______________
3) 35 + 28 (GCF=_____)
________________
6) 12 + 9
(GCF=_____)
________________
9) 24 + 18 (GCF=_____)
________________
12) 6 + 8
________________

4. Concept 1 Answer Key
Now let’s try one together:
2.
28
2
2.
45
14
5 9
2 7
3 3
22 7
3.
50
32 5
4.
72
5 10
8
2 5
9
2 4 3 3
2 2
2 52
23 32
Concept 2 Answer Key
GCF
GCF: 3 x 5 = 15
GCF= 15
GCF
GCF: 2 x 7 = 14
GCF = 14

5. Concept 3 Answer Key
Write each of the following sums as two factors of their GCF and a sum:
1) 24 + 16
4(6+4)
2) 25 + 15
5(5+3)
3) 35 + 28
7(5+4)
4) 63 + 54
9(7+6)
5) 80 + 30
10(8+3)
6) 12 + 9
3(4+3)
7) 54 + 36
18(3+2)
8) 49 + 84
7(7+12)
9) 24 + 18
6(4+3)
10) 20 + 44
4(5+11)
11) 4 + 12
4(1+3)
12) 6 + 8
2(3+4)

6. Name _______________________________________
Mrs. Labuski / Mrs. Portsmore Period ________
Date ____________________
FlashBack Homework
Concept1 & 2
Directions – Use Factor Trees& Venn Diagrams to find the GCF.
1) 36 and 60
2) 75 and 125
Concept 3 GCF & Distributive
Write each of the following sums as two factors of their GCF and a sum:
1) 22 + 16 (GCF=_____)
______________
4) 63 + 45 (GCF=_____)
______________
7) 54 + 18 (GCF=_____)
______________
10) 24 + 40
2) 35 + 20 (GCF=_____)
_______________
5) 70 + 40 (GCF=_____)
_______________
8) 49 + 98 (GCF=_____)
_______________
11) 20 + 24
3) 32 + 28 (GCF=_____)
________________
6) 18 + 42 (GCF=_____)
________________
9) 51 + 18 (GCF=_____)
________________
12) 49 + 63

7. ______________
_______________
________________