1.
To find the greatest number of identical bags an owner can make out of crayons, paintbrushes and oil paints.
1.
Answer to Problem 11E
Prime Factors of 225 are:3, 3, 5, 5.
Prime Factors of 75 are:3, 5, 5.
Prime Factors of 120 are:2,2,2, 3, 5.
Explanation of Solution
Given Information:
225 crayons, 75 paintbrushes and 120 tubes of oil paint.
Formula used: using greatest common factor
Calculation:
1. To get the Prime Factors of 225, divide 225 by the smallest prime number possible. Then take the result from that and divide that by the smallest prime number. Repeat this process until end up with 1.
This Prime Factorization process creates the Prime Factor Tree of 225. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 225. Here is the math to illustrate:
Again, all the prime numbers used to divide above are the Prime Factors of 225.
- Thus, the Prime Factors of 225 are:
- The Prime Factors of 75 are:
- The Prime Factors of 120 are:
3, 3, 5, 5.
Repeat the process for the other two numbers.
3, 5, 5.
2, 2, 2, 3, 5.
2.
To find GCF & Common Prime Factors
2.
Answer to Problem 11E
The common factors are: 1, 3, 5, 15
Then the greatest common factor is 15.
Explanation of Solution
Given Information:
225 crayons, 75 paintbrushes and 120 tubes of oil paint.
Formula used: using greatest common factor
Calculation:
The factors of 75 are: 1, 3, 5, 15, 25, 75
The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 225 are: 1, 3, 5, 9, 15, 25, 45, 75, 225
The common factors are: 1, 3, 5, 15
Then the greatest common factor is 15.
3.
To understand what the GCF represents
3.
Answer to Problem 11E
The greatest number of identical gift-bags that can be made out of 225 crayons, 75 paintbrushes and 120 tubes of oil paint
Explanation of Solution
Given Information:
225 crayons, 75 paintbrushes and 120 tubes of oil paint.
Formula used: using greatest common factor
Calculation:
The greatest common factor here represents the greatest number of identical gift-bags that can be made out of 225 crayons, 75 paintbrushes and 120 tubes of oil paint.
Chapter 4 Solutions
EP PRE-ALGEBRA,COMMON CORE-1 YEAR CODE
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