The answer key of the Eureka Math Lesson 23 Homework 4.3 can be found below. Feel free to check it out to find how many questions that you get right. If you get the wrong answer, you can just correct it. Make sure to not only check the answer but also to understand it since it is the most important thing.
- Explain your thinking or use division to answer the following.
a. Is 2 a factor of 72?
Answer: Yes, because 72 is even and 2 is a factor of all even numbers.
b. Is 2 a factor of 73?
Answer: No, because 73 is odd and 2 is not a factor of odd numbers.
c. Is 3 a factor of 72?
Answer: Yes, because 3 x 24 = 72.
d. Is 2 a factor of 60?
Answer: Yes, because 60 is even.
e. Is 6 a factor of 72?
Answer: Yes, because 6 x 12 = 72.
f. Is 4 a factor of 60?
Answer: Yes, because 4 x 15 = 60.
g. Is 5 a factor of 72?
Answer: No, because 72 does not have a 5 or 0 in the ones place.
h. Is 8 a factor if 60?
Answer: No, because there is a remainder.
2.Use the associative property to find more factors of 12 and 30.
a. 12 = 6 x 2 = (2 x 3) x 2 = 2 x (3 x 2) = 12
b. 30 = 6 x 5 = (2 x 3) x 5 = 2 x (3 x 5) = 2 x 15 = 30
3. In class, we used the associative property to show that when 6 is a factor, then 2 and 3 are factors, because 6 = 2 x 3. Use the fact that 10 = 5 x 2 to show that 2 and 5 are factors of 70, 80, and 90.
Answer:
70 – 10 x 7 = (2 x 5) x 7 = 2 x (5 x 7) = 2 x 35 = 70
80 = 10 x 8 = (2 x 5) x 8 = 2 x (5 x 8) = 2 x 40 = 80
90 = 10 x 9 = (2 x 5) x 9 = 2 x (5 x 9) = 2 x 45 = 90
4. The first statement is false. The second statement is true. Explain why using words, pictures, or numbers.
a. If a number has 2 and 6 as factors, then it has 12 as a factor.
b. If a number has 12 as a factor, then both 2 and 6 are factors.
Answer:
A is false because 2 and 6 are factors of 18, but 12 is not a factor of 18.
B is true because if 12 is a factor then 2 and 6 must also be factors since 12 = 2 x 6.
If the result is not that satisfying, do not be discouraged and keep practicing until you excel it.
Apart from the answer key of the Eureka Math Lesson 23 Homework 4.3, you might also need the answer key of the previous lesson. For everyone who really wants to know the answer key of the Eureka Math Lesson 22 Homework, here is everything for you:
- Record the factors of the given numbers as multiplication sentences and as a list in order from least to greatest. Classify each as prime (P) or composite (C). The first problem is done for you:
| Multiplication Sentences | Factors | P or C | |
| a. | 8
1 x 4 = 8 2 x 4 = 8 |
The factors of 8 are: 1, 2, 4, and 8. | C |
| b. | 10
1 x 10 = 10 2 x 5 = 10 |
The factors of 10 are: 1, 2, 5, 10. | C |
| c. | 11
1 x 11 = 11 |
The factors of 11 are: 1 and 11. | P |
| d. | 14
1 x 14 = 14 2 x 7 = 14 |
The factors of 14 are: 1, 2, 7, and 14. | C |
| e. | 17
1 x 17 = 17 |
The factors of 17 are: 1 and 17. | P |
| f. | 20
1 x 20 = 20 2 x 10 = 20 4 x 5 = 20 |
The factors of 20 are: 1, 2, 4, 5, 10, and 20. | C |
| g. | 22
1 x 22 = 22 2 x 11 = 22 |
The factors of 22 are: 1, 2, 11, and 22. | C |
| h. | 23
1 x 23 = 23 |
The factors of 23 are: 1 and 23. | C |
| i. | 25
1 x 25 = 25 5 x 5 = 25 |
The factors of 25 are: 1, 5, and 25. | C |
| j. | 26
1 x 26 = 26 2 x 13 = 26 |
The factors of 26 are: 1, 2, 13, and 26. | C |
| k. | 27
1 x 27 = 27 3 x 9 = 27 |
The factors of 27 are: 1, 3, 9, and 27. | C |
| l. | 28
1 x 28 = 28 2 x 14 = 28 4 x 7 = 28 |
The factors of 28 are: 1, 2, 4, 7, 14, and 28. | C |
- Find all factors for the following numbers and classify as prime or composite. Explain your classification of each as prime or composite.
Prime:
| Factor Pairs for 19 | |
| 1 | 19 |
There are only 2 factors.
Composite:
| Factors Pairs for 21 | |
| 1 | 21 |
| 3 | 7 |
There are more than 2 factors.
Composite:
| Factors Pairs for 24 | |
| 1 | 24 |
| 2 | 12 |
| 3 | 8 |
| 4 | 6 |
There are more than 2 factors.
- Bryan says that only even numbers are composite.
a. List all of the odd numbers less than 20 in numerical order.
Answer: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
b. Use your list to show that Bryan’s claim is false.
Answer: 9 and 15 are odd, but they are also composite.
- Julie has 27 grapes to divide evenly among 3 friends. She thinks there will be no leftovers. Use what you know about factor pairs to explain if Julie is correct.
Answer: Since 3 x 9 = 27, it can be concluded that there will be no leftovers.
