Factors & Arrays
What are all the factors of 12?
Answer: 1, 2, 3, 4, 6, and 12.
Is 13 prime or composite?
Answer: Prime. Its only factors are 1 and 13.
Complete the comparison: 24 is ___ times as many as 6.
Answer: 4 times, because 6 × 4 = 24.
There are 4 bags with 6 marbles in each bag. Write an equation to find the total n.
Answer: 4 × 6 = n, so n = 24.
What are the first five positive multiples of 7?
Answer: 7, 14, 21, 28, and 35.
A teacher puts 24 pencils into equal groups with none left over. Name three possible group sizes.
2 groups of 12, 3 groups of 8, 4 groups of 6 pencils per group.
Is 15 prime or composite? Explain why.
Answer: Composite. It has factors 1, 3, 5, and 15.
Write two comparisons shown by 5 × 8 = 40
Answer: 40 is 5 times as many as 8. 40 is 8 times as many as 5.
Mia has 7 stickers. Noah has 5 times as many. Write and solve an equation for Noah's stickers, n.
Answer: 7 × 5 = n; n = 35 stickers.
Which numbers are multiples of 6: 12, 16, 24, 28, 30?
Answer: 12, 24, and 30.
A student arranges 40 tiles into 5 equal rows. How many tiles are in each row?
Answer: 40 ÷ 5 = 8 tiles per row.
Name a prime number between 20 and 30.
Answer: 23 or 29.
Which equation shows that 7 is 3 times as many as a number n:
7 × 3 = n
3 × n = 7
7 + 3 = n
Answer: 3 × n = 7.
A park has 48 oak trees and 6 maple trees. How many times as many oak trees as maple trees are there? Write an equation.
Answer: 48 ÷ 6 = n; n = 8 times as many.
A bar model shows 4 equal sections, each worth 6. What is the total?
Answer: 4 × 6 = 24.
There are 36 cards. Give two different ways to arrange all the cards into equal rows, with at least 2 rows each.
Answer: Examples: 2 rows of 18, 3 rows of 12, 4 rows of 9, or 6 rows of 6.
A number has exactly two factors. What kind of number is it?
A prime number.
A blue ribbon is 9 inches long. A red ribbon is 4 times as long. How long is the red ribbon?
Answer: 9 × 4 = 36 inches.
A school collects 8 boxes of books and 8 boxes of games. Does 8 × 8 = n represent the total number of boxes? Explain.
Answer: No. The total is 8 + 8 = 16 boxes. Multiplication would represent equal groups, such as 8 groups of 8.
The Tigers score 5 times as many points as the Lions. The Tigers score 45 points. Write an equation to find the Lions' points, n, and solve.
Answer: 5 × n = 45, or 45 ÷ 5 = n. The Lions scored 9 points.
A number has exactly these factors: 1, 2, 4, 8, and 16. What is the number?
Answer: 16.
Which numbers are prime: 17, 21, 27, and 31?
17 and 31
Write two different comparison sentences for 6 × 9 = 54.
Answer: 54 is 6 times as many as 9. 54 is 9 times as many as 6.
A musician practices 4 hours one week and 6 times as many hours the next week. How many hours does the musician practice altogether?
Answer: 4 × 6 = 24 hours the next week;
24 + 4 = 28 hours total.
A number is a multiple of both 4 and 6. Give the smallest positive number that works and explain.
Answer: 12. It is 4 × 3 and 6 × 2.