Answer :
Sure! Let's break down the prime factorization of each number one by one:
a. 12
- Start with the smallest prime number, which is 2. Check if 12 can be divided by 2.
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 is a prime number, so we stop here.
- Therefore, the prime factorization is: 12 = 2 2 3
b. 32
- Divide 32 by 2 because it's the smallest prime.
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- Prime factorization: 32 = 2 2 2 2 2
c. 36
- Start with 2.
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 is not divisible by 2, so move to the next prime, which is 3.
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
- Prime factorization: 36 = 2 2 3 3
d. 40
- Start with 2.
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is a prime number, so we stop here.
- Prime factorization: 40 = 2 2 2 5
e. 44
- Start with 2.
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is a prime number, so we stop here.
- Prime factorization: 44 = 2 2 11
f. 56
- Start with 2.
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number, so we stop here.
- Prime factorization: 56 = 2 2 2 7
g. 45
- Start with the smallest odd prime (since 45 is odd), which is 3.
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is a prime number, so we stop here.
- Prime factorization: 45 = 3 3 5
h. 39
- 39 is not divisible by 2. Start with 3.
- 39 ÷ 3 = 13
- 13 is a prime number, so we stop here.
- Prime factorization: 39 = 3 13
i. 231
- 231 ÷ 3 = 77
- 77 ÷ 7 = 11
- 11 is a prime number, so we stop here.
- Prime factorization: 231 = 3 7 11
j. 63
- Start with 3.
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
- 7 is a prime number, so we stop here.
- Prime factorization: 63 = 3 3 7
I hope this breakdown makes the concept of prime factorization clearer! Let me know if you have any questions.
a. 12
- Start with the smallest prime number, which is 2. Check if 12 can be divided by 2.
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 is a prime number, so we stop here.
- Therefore, the prime factorization is: 12 = 2 2 3
b. 32
- Divide 32 by 2 because it's the smallest prime.
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
- Prime factorization: 32 = 2 2 2 2 2
c. 36
- Start with 2.
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 is not divisible by 2, so move to the next prime, which is 3.
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
- Prime factorization: 36 = 2 2 3 3
d. 40
- Start with 2.
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is a prime number, so we stop here.
- Prime factorization: 40 = 2 2 2 5
e. 44
- Start with 2.
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is a prime number, so we stop here.
- Prime factorization: 44 = 2 2 11
f. 56
- Start with 2.
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number, so we stop here.
- Prime factorization: 56 = 2 2 2 7
g. 45
- Start with the smallest odd prime (since 45 is odd), which is 3.
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is a prime number, so we stop here.
- Prime factorization: 45 = 3 3 5
h. 39
- 39 is not divisible by 2. Start with 3.
- 39 ÷ 3 = 13
- 13 is a prime number, so we stop here.
- Prime factorization: 39 = 3 13
i. 231
- 231 ÷ 3 = 77
- 77 ÷ 7 = 11
- 11 is a prime number, so we stop here.
- Prime factorization: 231 = 3 7 11
j. 63
- Start with 3.
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
- 7 is a prime number, so we stop here.
- Prime factorization: 63 = 3 3 7
I hope this breakdown makes the concept of prime factorization clearer! Let me know if you have any questions.
