Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A factor pair is two whole numbers that multiply to make a given number. The factor pairs of 24 are 1 and 24, 2 and 12, 3 and 8, and 4 and 6. Fourth graders find every factor pair for any whole number up to 100, usually by testing divisors in order and stopping once the pairs start to repeat. Arranging tiles into every possible rectangle is a helpful picture: each rectangle's side lengths form a factor pair.
The same fact can be described from the other side. If 6 is a factor of 24, then 24 is a multiple of 6. Students learn to decide whether a number up to 100 is a multiple of a one-digit number, using skip counting, multiplication facts or divisibility patterns. They also sort numbers into primes, which have exactly two factors (1 and themselves), and composites, which have more than two. The number 1 is neither prime nor composite because it has only one factor.
Numbers such as 9, 15, 21 and 27 are odd but composite. Ask students to test small divisors like 3 and 5 before calling an odd number prime.
Because 1 is only divisible by itself, students often call it prime. A prime must have exactly two different factors, and 1 has just one.
Students may list 12, 18 and 24 as factors of 6. Remind them that factors of a number are never larger than the number, while multiples never stop growing.
Listing factors randomly leads to gaps. Testing 1, 2, 3 and so on in order, and stopping when a pair repeats, finds every pair.
Find every factor pair of 36 and decide whether 36 is prime or composite.
Answer: The factor pairs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. With 9 factors, 36 is composite.
Square tiles are the best entry point. Give each pair of students a number of tiles, such as 18, and ask for every rectangle they can build. Numbers that only make a single long row (like 13 or 17) are prime, and that becomes the definition students remember.
A hundred chart lets students shade multiples of 2, 3, 5 and 7 and notice which numbers stay unshaded. Items on this standard often ask "Which number is a multiple of 7?" or "Which list shows all factors of 28?", so careful, ordered listing pays off.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) 1, 2, 4, 7, 14, 28
The factor pairs of 28 are 1 × 28, 2 × 14 and 4 × 7, so the factors are 1, 2, 4, 7, 14 and 28. 56 is a multiple, not a factor.
Answer: B) 29
29 has only the factors 1 and 29. 21 = 3 × 7, 27 = 3 × 9 and 33 = 3 × 11 are all composite.
Answer: A) 54
6 × 9 = 54. 38, 44 and 52 fall between multiples of 6 (36, 42, 48).
Answer: 2 (also accepted: two)
17 can only be made as 1 × 17, so its factors are 1 and 17. Two factors means 17 is prime.
Answer: 8
6 × 8 = 48, so 6 and 8 are a factor pair of 48.
Answer: B) It has exactly one factor
Primes have exactly two factors and composites have more than two. The number 1 has only one factor, itself, so it fits neither group.
Answer: 4 (also accepted: four)
1 × 24, 2 × 12, 3 × 8 and 4 × 6. That is 4 factor pairs.
A full lesson with slides, activities and an exit ticket on factors, multiples, primes and composites, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.OA.B.4 with an answer key, ready in about a minute.
Make a worksheet →Turn factors, multiples, primes and composites into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A factor divides into a number evenly; a multiple is what you get when you multiply a number by a whole number. 4 is a factor of 20, and 20 is a multiple of 4.
Yes. 2 has exactly two factors, 1 and 2, so it is prime. It is the only even prime, because every other even number also has 2 as a factor.