This grade 4 factors worksheet answer key solves all 22 problems of the factors, multiples, primes and composites worksheet step by step.
This answer key gives a full worked solution for every problem on the factors and multiples worksheet. Compare your lists with the ones here, and check any factor pair by multiplying the two numbers together.
Grade 4 Factors Worksheet Answer Key: problems 1–5
Problem 1: First eight multiples of 3
Skip count by 3: \(3, 6, 9, 12, 15, 18, 21, 24\).
\(3, 6, 9, 12, 15, 18, 21, 24\)
Problem 2: Rectangles of 18 squares
The sentences are \(1 \times 18 = 18\), \(2 \times 9 = 18\), and \(3 \times 6 = 18\).
Read the factors from the pairs and put them in order.
Factors of 18: \(1, 2, 3, 6, 9, 18\)
Problem 3: Is 7 a factor?
\(7 \times 6 = 42\), so 7 divides 42 exactly.
\(7 \times 6 = 42\) and \(7 \times 7 = 49\), so 45 falls between two multiples of 7.
Yes for 42; no for 45.
Problem 4: Factors of 20
Pairs: \(1 \times 20\), \(2 \times 10\), \(4 \times 5\).
\(1, 2, 4, 5, 10, 20\)
Problem 5: Multiples of 6 below 40
Skip count by 6 and stop before 40: \(6, 12, 18, 24, 30, 36\). The next one, 42, is too big.
\(6, 12, 18, 24, 30, 36\)
Grade 4 Factors Worksheet Answer Key: problems 6–10
Problem 6: Multiple of 8?
\(8 \times 7 = 56\), so 56 is a multiple of 8.
The multiples of 8 near 58 are 56 and 64, so 58 is not one.
56: yes. 58: no.
Problem 7: Factor pairs of 28
Test 1, 2, 3, 4, 5. The numbers 1, 2, and 4 divide 28. After 4 the partner is 7, and 5 does not work, so stop.
\(1 \times 28\), \(2 \times 14\), \(4 \times 7\)
Problem 8: Prime or composite?
13 has only the pair \(1 \times 13\), so it is prime.
\(3 \times 7 = 21\), so 21 is composite.
29 has only the pair \(1 \times 29\), so it is prime.
\(3 \times 17 = 51\), so 51 is composite.
13 prime, 21 composite, 29 prime, 51 composite.
Problem 9: Hops on a number line
Each hop adds 7: \(0, 7, 14, 21, 28\). Then \(28 + 7 = 35\) and \(35 + 7 = 42\).
The next mark is \(42 + 7 = 49\), which is \(7 \times 7\).
Rule: add 7. Missing: 35 and 42. Yes, 49 comes next.
Problem 10: Multiples of 9 on a chart
Skip count by 9: \(9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99\).
The digits of each number add to 9 (for example, \(2 + 7 = 9\)), and \(9 + 9 = 18\) for 99, which is also a multiple of 9.
11 multiples; the digits add to 9 or 18.
Grade 4 Factors Worksheet Answer Key: problems 11–15
Problem 11: Factors of 45
Pairs: \(1 \times 45\), \(3 \times 15\), \(5 \times 9\).
\(1, 3, 5, 9, 15, 45\)
Problem 12: Multiples of 4
\(4 \times 6 = 24\), \(4 \times 12 = 48\), \(4 \times 13 = 52\), \(4 \times 15 = 60\). The number 35 is not a multiple (\(4 \times 8 = 32\) and \(4 \times 9 = 36\)).
\(24, 48, 52, 60\)
Problem 13: Factor pairs of 64
Test 1, 2, 4, 8. The numbers 3, 5, 6, and 7 do not divide 64. At 8 the partner is 8, so stop.
\(1 \times 64\), \(2 \times 32\), \(4 \times 16\), \(8 \times 8\); the pair \(8 \times 8\) uses 8 twice.
Problem 14: Missing factor
Skip count by 9: 9, 18, 27, 36, 45, 54, 63, 72. That is 8 jumps, so \(9 \times 8 = 72\).
The missing number is 8, and 72 is a multiple of 9.
Problem 15: Sort the numbers
11 and 37 have only 1 and themselves as factors.
\(3 \times 9 = 27\), \(7 \times 7 = 49\), \(3 \times 19 = 57\), \(7 \times 13 = 91\).
Prime: \(11, 37\). Composite: \(27, 49, 57, 91\).
Grade 4 Factors Worksheet Answer Key: problems 16–20
Problem 16: Arrays and primes
Five dots can only be arranged as 1 row of 5, so the only factor pair is \(1 \times 5\). That gives exactly two factors, 1 and 5.
Six dots make a 1 by 6 array and also a 2 by 3 array. The factors are \(1, 2, 3, 6\), which is more than two.
5 is prime (2 factors); 6 is composite (4 factors).
Problem 17: Mystery number
Multiples of 7: 42, 49, 56, 63. Only 56 is between 50 and 60.
56
Problem 18: Setting up chairs
Test 1, 2, 3, 4, 5. The numbers 1, 2, 3, and 5 divide 30. The pairs are \(1 \times 30\), \(2 \times 15\), \(3 \times 10\), \(5 \times 6\).
Each pair gives one arrangement, and 4 does not divide 30.
4 arrangements: 1 by 30, 2 by 15, 3 by 10, and 5 by 6.
Problem 19: Cookie boxes
The factors of 48 are \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\). The ones from 4 to 12 are \(4, 6, 8, 12\).
\(48 : 4 = 12\), \(48 : 6 = 8\), \(48 : 8 = 6\), \(48 : 12 = 4\).
4, 6, 8, or 12 cookies per box, using 12, 8, 6, or 4 boxes.
Problem 20: Saving in the jar
The amounts are multiples of 6: \(\$6, \$12, \$18, \$24, \$30, \$36, \$42, \$48, \$54, \$60\).
50 is between \(\$48\) and \(\$54\), so it is not a multiple of 6. And \(6 \times 9 = 54\).
Not $50. Yes, $54, after week 9.
Grade 4 Factors Worksheet Answer Key: problems 21–22
Problem 21: Priya's claim
Try 3: the digits add to \(5 + 1 = 6\), a multiple of 3. \(3 \times 17 = 51\).
So 51 has the factors \(1, 3, 17, 51\), which is more than two.
No. 51 is composite because \(3 \times 17 = 51\).
Problem 22: Sticker pages
The factors of 72 are \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\). Those from 2 to 10 are \(2, 3, 4, 6, 8, 9\). The number 5 and the number 7 do not divide 72.
\(72 : 2 = 36\), \(72 : 3 = 24\), \(72 : 4 = 18\), \(72 : 6 = 12\), \(72 : 8 = 9\), \(72 : 9 = 8\).
2, 3, 4, 6, 8, or 9 stickers per page, using 36, 24, 18, 12, 9, or 8 pages.
How to use this grade 4 factors worksheet answer key
Read this grade 4 factors worksheet answer key after trying each problem yourself, and redo any problem you missed.
See every chapter on the Grade 4 math page.