4th Grade Factors, Multiples, Prime and Composite Worksheet Solutions (PDF)

Try each number from 1 up: \(1 \times 12 = 12\), \(2 \times 6 = 12\), \(3 \times 4 = 12\). Next, 4 is already used, so stop.

Factor pairs: 1 and 12, 2 and 6, 3 and 4.

Pairs: \(1 \times 18\), \(2 \times 9\), \(3 \times 6\). 4 and 5 do not divide 18 evenly, and 6 is already listed.

Factors: 1, 2, 3, 6, 9, 18.

Skip count by 7: 7, 14, 21, 28, 35, 42.

Check: \(7 \times 6 = 42\). The multiples are 7, 14, 21, 28, 35, 42.

There are 5 rows of 6 tiles: \(5 \times 6 = 30\).

Factor pairs of 30: \(1 \times 30\), \(2 \times 15\), \(3 \times 10\), \(5 \times 6\).

Answer: \(5 \times 6 = 30\); pairs 1 and 30, 2 and 15, 3 and 10, 5 and 6.

Divide: \(54 \div 6 = 9\) with no remainder, or \(6 \times 9 = 54\).

Yes, 6 is a factor of 54.

(a) \(8 \times 7 = 56\), so 56 is a multiple of 8.

(b) \(8 \times 7 = 56\) and \(8 \times 8 = 64\), so 58 falls between two multiples.

Answer: (a) yes, (b) no.

Check each: \(4 \times 5 = 20\), \(4 \times 8 = 32\), \(4 \times 11 = 44\). The numbers 14, 26 and 38 leave a remainder of 2 when divided by 4.

Multiples of 4: 20, 32, 44.

Each jump is 8. After 16 comes \(16 + 8 = 24\). After 32 comes \(32 + 8 = 40\). After 56 comes \(56 + 8 = 64\).

Missing numbers: 24, 40, 64.

7 has factors 1 and 7 only: prime. 9 has factors 1, 3, 9: composite. 11 has factors 1 and 11 only: prime. 15 has factors 1, 3, 5, 15: composite.

Answer: 7 prime, 9 composite, 11 prime, 15 composite.

Remove the even numbers and the multiples of 5. Then test the rest: 21 = \(3 \times 7,\) 27 = \(3 \times 9,\) 33 = \(3 \times 11,\) 39 = \(3 \times 13\) are composite. 25 is a multiple of 5.

What is left: 23, 29, 31, 37.

Primes: 23, 29, 31, 37.

Any even number is a multiple of 2. If it is greater than 2, it has the factors 1, 2 and itself, so it has at least three factors and is composite. The number 2 has just the factors 1 and 2.

Answer: 2 has exactly two factors, and every larger even number has at least three.

The last digit is 5.

(a) 5 is not 0, 2, 4, 6 or 8, so not divisible by 2.

(b) The last digit is 5, so divisible by 5.

(c) The last digit is not 0, so not divisible by 10.

Answer: (a) no, (b) yes, (c) no.

\(1 \times 36\), \(2 \times 18\), \(3 \times 12\), \(4 \times 9\), \(6 \times 6\). The factor 6 is counted once.

Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Answer: 5 factor pairs, 9 factors.

Pairs: \(1 \times 48\), \(2 \times 24\), \(3 \times 16\), \(4 \times 12\), \(6 \times 8\). 5 and 7 do not divide 48.

Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 (10 factors).

Row lengths are the factors of 28. Pairs: \(1 \times 28\), \(2 \times 14\), \(4 \times 7\). (5 and 3 do not work.)

Row lengths: 1, 2, 4, 7, 14, 28.

The totals must be multiples of 6. \(6 \times 7 = 42\) and \(6 \times 9 = 54\). For 50: \(6 \times 8 = 48\), remainder 2. For 62: \(6 \times 10 = 60\), remainder 2.

Answer: 42 and 54.

Team sizes must be factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.

Keep sizes from 2 to 10: 2, 3, 5, 6, 10.

Answer: 2, 3, 5, 6 or 10 players per team.

Add 15 minutes each time. After 8:45 come 9:00, 9:15 and 9:30.

9:30 AM is 90 minutes after 8:00, and \(15 \times 6 = 90\), so it is a multiple of 15.

Answer: 9:00, 9:15, 9:30; yes, a bus leaves at 9:30.

Primes between 40 and 50: 41, 43, 47 (42, 44, 46, 48, 50 are even, 45 is a multiple of 5, 49 = \(7 \times 7\)).

Digit sums: 4 + 1 = 5, 4 + 3 = 7, 4 + 7 = 11.

Answer: 47.

Try 3: \(3 \times 17 = 51\). So 51 has the factors 1, 3, 17 and 51.

A prime number has only two factors, so 51 is composite.

Answer: No. 51 = \(3 \times 17,\) so it is composite.