All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 1 Prime Factorization will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 1 Prime Factorization
Talk Math
What are the first ten prime numbers?
Guided Practice
Question 1.
Find the prime factorization of 16.
The prime factorization of 16 is
____ × ____ × ____ × ____
Answer:
2 × 2 × 2 × 2
Explanation:
Independent Practice
Find the prime factorization of each number.
Question 2.
63 = ___
Answer:
3 × 3 × 7 = 32 × 7
Explanation:
Question 3.
18 = ____
Answer:
2 × 3 × 3
Explanation:
Question 4.
40 = ___
Answer:
2 × 2 × 2 × 5
Explanation:
Question 5.
75 = ____
Answer:
3 × 5 × 5
Explanation:
Question 6.
27 = ___
Answer:
3 × 3 × 3
Explanation:
Question 7.
32 = ____
Answer:
2 × 2 × 2 × 2
Explanation:
Question 8.
49 = ____
Answer:
7 × 7
Explanation:
Question 9.
44 = ____
Answer:
11 × 4
11 × 2 × 2
Explanation:
Mathematical PRACTICE 2 Understand Symbols Find the missing number.
Question 10.
104 = 2 × 2 × × 13
= ___
Answer:
x = 2
Explanation:
Let us solve the expression to find the missing number
104 = 2 × 2 × x × 13
104 = 4 × x × 13
104 = 52x
x = 104 ÷ 52
x = 2
Question 11.
55 = × 11
= ___
Answer:
x = 5
Explanation:
Let us solve the expression to find the missing number
55 = x × 11
x = 55 ÷ 11
x = 5
Question 12.
77 = 7 ×
= ___
Answer:
x = 11
Explanation:
Let us solve the expression to find the missing number
77 = 7 × x
x = 77 ÷ 7
x = 11
Problem Solving
Use the table for Exercises 13—16 that shows the average weights of popular dog breeds.
Question 13.
Complete the table.
Answer:
Question 14.
Which weight(s) have a prime factorization of exactly three factors?
Answer:
The weights of cocker spaniel, Golden Retriever, and Siberian Husky.
Question 15.
Which weight(s) have a prime factorization with factors that are all the same number?
Answer:
Beagle
Explanation:
The weight of Beagle has factors that are all the same number.
Beagle 5 × 5
Question 16.
Which breed(s) have weights that are prime numbers?
Answer:
Labrador Retriever.
Explanation:
Labrador Retriever have weights that are prime numbers.
Hot Problems
Question 17.
Mathematical PRACTICE Identify Structure Find the prime factorization of 2,800.
Answer:
The prime factorization of 2,800 is 24 × 52 × 71
Explanation:
The prime factorization is 24 × 52 × 71
Question 18.
? Building on the Essential Question How do factor trees help you find the prime factorization of a number?
Answer:
First write the given number at the top of the factor tree and and draw two branches.
write the pair of branches with a pair of factor of the number above
Continue this step until each branch ends with a prime number.
Write the solution in a separate line.
McGraw Hill My Math Grade 5 Chapter 2 Lesson 1 My Homework Answer Key
Practice
Find the prime factorization of each number.
Question 1.
50 = ____
Answer:
2 × 5 × 5
Explanation:
The prime factorization of the given number is 2 × 5 × 5.
Question 2.
81 = ___
Answer:
3 × 3 × 3 × 3
Explanation:
The prime factorization of the given number is 3 × 3 × 3 × 3
Question 3.
65 = ___
Answer:
5 × 13
Explanation:
The prime factorization of the given number is 5 × 13.
Question 4.
28 = ___
Answer:
2 × 2 × 7
Explanation:
The prime factorization of the given number is 2 × 2 × 7.
Problem Solving
Question 5.
Britney scored an 85 on her last math test. Write the prime factorization of 85.
Answer:
5 × 17
Explanation:
The prime factorization of 85 is 5 × 17.
Question 6.
Priscilla has 56 stickers in her collection. Write the prime factorization of 56.
Answer:
2 × 2 × 2 × 7
Explanation:
Given 56
we need to find the prime factorization.
Factor of 56
56 = 1 × 56, 2 × 28, 4× 14, 7 × 8
56 = 2 × 2 × 2 × 7
Question 7.
Mathematical PRACTICE 3 Find the Error Lainey wrote the prime factorization of 60 as 2 × 5 × 6. Is she correct? If not, what is the prime factorization of 60? Explain.
Answer:
She is not correct because 6 is not a prime number.
2 × 2 × 5 × 3
Explanation:
She is not correct because 6 is not a prime. It is a composite number. The answer for the prime factorization is 2 × 2 × 5 × 3.
Vocabulary Check
Fill in each blank with the correct term or number to complete the sentence.
Question 8.
___ numbers can be written as a product of factors. This is called the prime factorization of a number.
Answer:
Composite number.
Explanation:
Composite numbers can be written as a product of factors. This is called the prime factorization of a number.
Test Practice
Question 9.
Josiah had a pot belly pig as a pet that weighed 46 pounds. What is the prime factorization of 46?
A. 2 × 23
B. 2 × 2 × 11
C. 2 × 2 × 13
D. 3 × 23
Answer:
46 = 2 × 23
Explanation:
Josiah had a pot belly pig as a pet that weighed 46 pounds
Factors of 46 are 1, 2, 23 and 46
Prime factors = 2 and 23
The prime factorization of 46 is 46 = 2 × 23