To find the prime factors of a number, we break it down into smaller numbers that multiply together to make the original number. We keep breaking them down until all the numbers are
prime (numbers that can only be divided by 1 and themselves, like 2, 3, 5, 7, 11).
Here is the step-by-step breakdown for each problem:
2. 35
* 35 ends in 5, so it is divisible by 5.
* $35 \div 5 = 7$.
* 7 is a prime number.
* Prime factors:
5 x 7
3. 54
* 54 is even, so divide by 2: $54 \div 2 = 27$.
* 27 is not even, but $2 + 7 = 9$, so it is divisible by 3: $27 \div 3 = 9$.
* 9 is divisible by 3: $9 \div 3 = 3$.
* 3 is prime.
* Prime factors:
2 x 3 x 3 x 3
4. 48
* 48 is even: $48 \div 2 = 24$.
* 24 is even: $24 \div 2 = 12$.
* 12 is even: $12 \div 2 = 6$.
* 6 is even: $6 \div 2 = 3$.
* 3 is prime.
* Prime factors:
2 x 2 x 2 x 2 x 3
5. 14
* 14 is even: $14 \div 2 = 7$.
* 7 is prime.
* Prime factors:
2 x 7
6. 50
* 50 is even: $50 \div 2 = 25$.
* 25 ends in 5: $25 \div 5 = 5$.
* 5 is prime.
* Prime factors:
2 x 5 x 5
7. 36
* 36 is even: $36 \div 2 = 18$.
* 18 is even: $18 \div 2 = 9$.
* 9 is divisible by 3: $9 \div 3 = 3$.
* 3 is prime.
* Prime factors:
2 x 2 x 3 x 3
8. 68
* 68 is even: $68 \div 2 = 34$.
* 34 is even: $34 \div 2 = 17$.
* 17 is a prime number.
* Prime factors:
2 x 2 x 17
9. 32
* 32 is even: $32 \div 2 = 16$.
* 16 is even: $16 \div 2 = 8$.
* 8 is even: $8 \div 2 = 4$.
* 4 is even: $4 \div 2 = 2$.
* 2 is prime.
* Prime factors:
2 x 2 x 2 x 2 x 2
10. 40
* 40 is even: $40 \div 2 = 20$.
* 20 is even: $20 \div 2 = 10$.
* 10 is even: $10 \div 2 = 5$.
* 5 is prime.
* Prime factors:
2 x 2 x 2 x 5
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Final Answer:
2. 5 x 7
3. 2 x 3 x 3 x 3
4. 2 x 2 x 2 x 2 x 3
5. 2 x 7
6. 2 x 5 x 5
7. 2 x 2 x 3 x 3
8. 2 x 2 x 17
9. 2 x 2 x 2 x 2 x 2
10. 2 x 2 x 2 x 5
Parent Tip: Review the logic above to help your child master the concept of prime factors worksheet 6th grade.
