QuestionPRNGIC Write the prime factorization of the number. If the number is prime, write prime.
1. 42
2. 104
3. 75
4. 23
6. 27
7. 72 a. 180
9. 47
11. 88
12. 49
13. 83
14. 142

Studdy Solution
Continue factorization of 25: $25 = 5 \times 5$
STEP_{10}: Combine the factors: $75 = 3 \times 5^2$
STEP_{11}: Determine if 23 is prime. Since 23 has no divisors other than 1 and itself, it is prime.
STEP_{12}: Prime factorization of 27: $27 = 3 \times 9$
STEP_{13}: Continue factorization of 9: $9 = 3 \times 3$
STEP_{14}: Combine the factors: $27 = 3^3$
STEP_{15}: Prime factorization of 72: $72 = 2 \times 36$
STEP_{16}: Continue factorization of 36: $36 = 2 \times 18$
STEP_{17}: Continue factorization of 18: $18 = 2 \times 9$
STEP_{18}: Continue factorization of 9: $9 = 3 \times 3$
STEP_{19}: Combine the factors: $72 = 2^3 \times 3^2$
STEP_{20}: Prime factorization of 180: $180 = 2 \times 90$
STEP_{21}: Continue factorization of 90: $90 = 2 \times 45$
STEP_{22}: Continue factorization of 45: $45 = 3 \times 15$
STEP_{23}: Continue factorization of 15: $15 = 3 \times 5$
STEP_{24}: Combine the factors: $180 = 2^2 \times 3^2 \times 5$
STEP_{25}: Determine if 47 is prime. Since 47 has no divisors other than 1 and itself, it is prime.
STEP_{26}: Prime factorization of 88: $88 = 2 \times 44$
STEP_{27}: Continue factorization of 44: $44 = 2 \times 22$
STEP_{28}: Continue factorization of 22: $22 = 2 \times 11$
STEP_{29}: Combine the factors: $88 = 2^3 \times 11$
STEP_{30}:0 Prime factorization of 49: $49 = 7 \times 7$
STEP_{31}:1 Determine if 83 is prime. Since 83 has no divisors other than 1 and itself, it is prime.
STEP_{32}:2 Prime factorization of 142: $142 = 2 \times 71$
Solution:
1. $42 = 2 \times 3 \times 7$
2. $104 = 2^3 \times 13$
3. $75 = 3 \times 5^2$
4. $23$ is prime.
5. $27 = 3^3$
6. $72 = 2^3 \times 3^2$
7. $180 = 2^2 \times 3^2 \times 5$
8. $47$ is prime.
9. $88 = 2^3 \times 11$
10. $49 = 7^2$
11. $83$ is prime.
12. $142 = 2 \times 71$