Download Prime Factorizations, GCF`s and LCM`s # 1 - 3

Factors and Multiples of Whole Numbers
The prime factorization of a natural number is the number written as a product of its prime factors.
1. Write the prime factorization of 2450 by using a factor tree.
What are the prime factors of 2450? _____________________________
What is the prime factorization of 2450?_____________________ or ______________________
What other factors did you identify for 2450? _________________________________________
2. The Greatest Common Factor (GCF) of two or more numbers is the largest number that will
divide into those numbers.
Determine the GCF of 108 and 48.
3. The Least Common Multiple (LCM) of two or more numbers is the smallest number that is
divisible by each number.
Determine the LCM of 10 and 12.
Using Prime Factorization to Find the GCF and LCM
4. Look for a pattern with the prime factorizations that will allow you to use prime factorizations to
determine the GCF. Repeat for the LCM. Use the patterns to complete the chart.
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8.
1st Number
2nd Number
Greatest
Common Factor
Least Common
Multiple
Standard Form
15
25
5
75
Prime
Factorization
3×5
52
5
3×52
Standard Form
12
18
6
36
Prime
Factorization
22×3
2×32
2×3
22×32
Standard Form
245
1029
49
5145
Prime
Factorization
5×72
3×73
72
3×5×73
Standard Form
90
70
10
630
Prime
Factorization
2×32×5
2×5×7
2×5
2×32×5×7
Standard Form
3087
315
63
15 435
Prime
Factorization
32×73
32×7×5
32×7
32×73×5
Standard Form
108
48
Prime
Factorization
22×33
24×3
Standard Form
12
10
Prime
Factorization
22×3
2×5
Standard Form
4725
126
Prime
Factorization
5. Describe how to determine the Greatest Common Factor using Prime Factorization:
e.g., Use prime factorization to find the GCF of the set of numbers 120, 160, 180.
6. Describe how to determine the Least Common Multiple using Prime Factorization:
e.g., Use prime factorization to find the LCM of the set of numbers 120, 160, 180.