FACTORS AND FACTOR PAIRS
Name two factor pairs of 12
1x12, 2x6, or 3x4
Is 7 prime or composite? Explain why.
7 is prime (only factors (1,7)).
Fill in the blank: 6×__=30
6×5=30 so the missing factor is 5.
True or False: Every even number is composite
False — for example, 2 is even and prime.
Maria has 12 apples and wants to put them into equal groups with no apples left over. What are two ways she can group the apples? (Give the group sizes and how many groups for each.)
Ways to group 12 apples:
List all the factor pairs of 24
1x24, 2x12, 3x8, 4x6
Is 21 prime or composite? Give its factor pair that proves your answer.
21 is composite; factors include (3,7).
Fill in the blank: __×8=56
7×8=56 so the missing factor is 7.
True or False: If a number has exactly two factors, it is prime.
True — numbers with exactly two distinct factors (1 and itself) are prime.
A gardener plants 24 flowers in rows so each row has the same number of flowers and no flowers are left over. List all the possible numbers of flowers per row.
Possible flowers per row for 24: 1,2,3,4,6,8,12,24 (from factor pairs).
Explain why 1 and the number itself are always a factor pair for any whole number greater than 1. Give an example using 18.
Because multiplying any number by 1 gives the number, (1 x n) is a factor pair; example for 18: (1x18)
Which is the smallest composite number greater than 1? Explain
Smallest composite greater than 1 is 4 (factors (1,4),(2,2)); note that 2 and 3 are prime.
A number times 9 equals 81. What is the missing factor?
9×9=81 so the missing factor is 9.
True or False: All multiples of 5 end in 5 or 0 — explain how this helps find factors of numbers that end in 5 or 0.
True — multiples of 5 end in 5 or 0; this helps because if a number ends in 5 or 0, 5 is a factor.
A ribbon is 36 inches long. Sarah cuts it into equal pieces so none is wasted. If she chooses to cut pieces that are 4 inches long, how many pieces does she get? Show the factor pair you used.
36÷4=9 so Sarah gets 9 pieces; factor pair used (4,9).
A rectangle has area 36 square units. If one side is 4 units long, what is the length of the other side? Show the factor pair you used.
Other side is 9 because 4×9=36; factor pair (4,9)
Decide whether 1 is prime, composite, or neither. Explain your reasoning in one sentence.
1 is neither prime nor composite because it has only one factor.
If __×7=91, what is the missing factor? Show how you know.
13×7=91 so the missing factor is 13.
True or False: A number with factors 1,2,4,8 is prime. Explain your answer.
False — those factors show the number has more than two factors, so it is composite.
A classroom has 28 desks. The teacher wants to arrange them in equal rows with the same number of desks in each row. Give two different arrangements that use all desks and explain how you found them using factor pairs.
Two arrangements for 28 desks:
Find all factor pairs of 48 and write them in order from smallest to largest first factor.
Factor pairs of 48: (1,48),(2,24),(3,16),(4,12),(6,8).
For each number, say "prime" or "composite" and give a short reason: 29,35,49,2.
29 — prime (no divisors besides 1 and 29); 35 — composite (factors (5,7)); 49 — composite (factors (7,7)); 2 — prime (factors (1,2))
A product is 144. One factor is 12. What is the other factor? Explain how you found it and list both factor pairs that include 12.
144÷12=12 so the other factor is 12; factor pairs involving 12: (12,12) and full factor pairs of 144 include (1,144),(2,72),(3,48),(4,36),(6,24),(8,18),(9,16),(12,12).
True or False: If a number is not divisible by 2, 3, or 5, then it must be prime. Explain why this statement is or is not true and give an example to support your answer.
False — not divisible by 2, 3, or 5 does not guarantee prime (counterexample: 49 is not divisible by 2,3,5 but is composite because 7×7=49).
A pack contains 48 stickers. Four friends want to share them so each friend gets the same number and none are left over. What are all the ways they could share the stickers among friends (use factor pairs of 48) and explain which sharing options have more than two friends getting stickers.
(1,48) — 1 friend (not a split), (2,24) — 2 friends get 24 each, (3,16) — 3 friends get 16 each, (4,12) — 4 friends get 12 each, (6,8) — 6 friends get 8 each, (8,6), (12,4), (16,3), (24,2), (48,1) correspond to the same splits reversed. Sharing with more than two friends: splits like 3, 4, 6, 8, 12, 16, 24 friends are possible (choose the factor where the first number is the number of friends).