Answer :
Sure, let's break down each number into its prime factors step-by-step.
### e. 78
To factorize 78 into prime factors:
1. 78 is divisible by 2:
[tex]\(78 \div 2 = 39\)[/tex]
Prime factor: 2
2. 39 is divisible by 3:
[tex]\(39 \div 3 = 13\)[/tex]
Prime factor: 3
3. 13 is a prime number.
Prime factor: 13
So, the prime factorization of 78 is:
[tex]\[ 78 = 2 \times 3 \times 13 \][/tex]
### f. 46
To factorize 46 into prime factors:
1. 46 is divisible by 2:
[tex]\(46 \div 2 = 23\)[/tex]
Prime factor: 2
2. 23 is a prime number.
Prime factor: 23
So, the prime factorization of 46 is:
[tex]\[ 46 = 2 \times 23 \][/tex]
### b. 48
To factorize 48 into prime factors:
1. 48 is divisible by 2:
[tex]\(48 \div 2 = 24\)[/tex]
Prime factor: 2
2. 24 is divisible by 2:
[tex]\(24 \div 2 = 12\)[/tex]
Prime factor: 2
3. 12 is divisible by 2:
[tex]\(12 \div 2 = 6\)[/tex]
Prime factor: 2
4. 6 is divisible by 2:
[tex]\(6 \div 2 = 3\)[/tex]
Prime factor: 2
5. 3 is a prime number.
Prime factor: 3
So, the prime factorization of 48 is:
[tex]\[ 48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3 \][/tex]
### c. 38
To factorize 38 into prime factors:
1. 38 is divisible by 2:
[tex]\(38 \div 2 = 19\)[/tex]
Prime factor: 2
2. 19 is a prime number.
Prime factor: 19
So, the prime factorization of 38 is:
[tex]\[ 38 = 2 \times 19 \][/tex]
### g. 50
To factorize 50 into prime factors:
1. 50 is divisible by 2:
[tex]\(50 \div 2 = 25\)[/tex]
Prime factor: 2
2. 25 is divisible by 5:
[tex]\(25 \div 5 = 5\)[/tex]
Prime factor: 5
3. 5 is a prime number.
Prime factor: 5
So, the prime factorization of 50 is:
[tex]\[ 50 = 2 \times 5 \times 5 = 2 \times 5^2 \][/tex]
### d. 62
To factorize 62 into prime factors:
1. 62 is divisible by 2:
[tex]\(62 \div 2 = 31\)[/tex]
Prime factor: 2
2. 31 is a prime number.
Prime factor: 31
So, the prime factorization of 62 is:
[tex]\[ 62 = 2 \times 31 \][/tex]
### h. 88
To factorize 88 into prime factors:
1. 88 is divisible by 2:
[tex]\(88 \div 2 = 44\)[/tex]
Prime factor: 2
2. 44 is divisible by 2:
[tex]\(44 \div 2 = 22\)[/tex]
Prime factor: 2
3. 22 is divisible by 2:
[tex]\(22 \div 2 = 11\)[/tex]
Prime factor: 2
4. 11 is a prime number.
Prime factor: 11
So, the prime factorization of 88 is:
[tex]\[ 88 = 2 \times 2 \times 2 \times 11 = 2^3 \times 11 \][/tex]
I hope this helps! Let me know if you have any other questions.
### e. 78
To factorize 78 into prime factors:
1. 78 is divisible by 2:
[tex]\(78 \div 2 = 39\)[/tex]
Prime factor: 2
2. 39 is divisible by 3:
[tex]\(39 \div 3 = 13\)[/tex]
Prime factor: 3
3. 13 is a prime number.
Prime factor: 13
So, the prime factorization of 78 is:
[tex]\[ 78 = 2 \times 3 \times 13 \][/tex]
### f. 46
To factorize 46 into prime factors:
1. 46 is divisible by 2:
[tex]\(46 \div 2 = 23\)[/tex]
Prime factor: 2
2. 23 is a prime number.
Prime factor: 23
So, the prime factorization of 46 is:
[tex]\[ 46 = 2 \times 23 \][/tex]
### b. 48
To factorize 48 into prime factors:
1. 48 is divisible by 2:
[tex]\(48 \div 2 = 24\)[/tex]
Prime factor: 2
2. 24 is divisible by 2:
[tex]\(24 \div 2 = 12\)[/tex]
Prime factor: 2
3. 12 is divisible by 2:
[tex]\(12 \div 2 = 6\)[/tex]
Prime factor: 2
4. 6 is divisible by 2:
[tex]\(6 \div 2 = 3\)[/tex]
Prime factor: 2
5. 3 is a prime number.
Prime factor: 3
So, the prime factorization of 48 is:
[tex]\[ 48 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3 \][/tex]
### c. 38
To factorize 38 into prime factors:
1. 38 is divisible by 2:
[tex]\(38 \div 2 = 19\)[/tex]
Prime factor: 2
2. 19 is a prime number.
Prime factor: 19
So, the prime factorization of 38 is:
[tex]\[ 38 = 2 \times 19 \][/tex]
### g. 50
To factorize 50 into prime factors:
1. 50 is divisible by 2:
[tex]\(50 \div 2 = 25\)[/tex]
Prime factor: 2
2. 25 is divisible by 5:
[tex]\(25 \div 5 = 5\)[/tex]
Prime factor: 5
3. 5 is a prime number.
Prime factor: 5
So, the prime factorization of 50 is:
[tex]\[ 50 = 2 \times 5 \times 5 = 2 \times 5^2 \][/tex]
### d. 62
To factorize 62 into prime factors:
1. 62 is divisible by 2:
[tex]\(62 \div 2 = 31\)[/tex]
Prime factor: 2
2. 31 is a prime number.
Prime factor: 31
So, the prime factorization of 62 is:
[tex]\[ 62 = 2 \times 31 \][/tex]
### h. 88
To factorize 88 into prime factors:
1. 88 is divisible by 2:
[tex]\(88 \div 2 = 44\)[/tex]
Prime factor: 2
2. 44 is divisible by 2:
[tex]\(44 \div 2 = 22\)[/tex]
Prime factor: 2
3. 22 is divisible by 2:
[tex]\(22 \div 2 = 11\)[/tex]
Prime factor: 2
4. 11 is a prime number.
Prime factor: 11
So, the prime factorization of 88 is:
[tex]\[ 88 = 2 \times 2 \times 2 \times 11 = 2^3 \times 11 \][/tex]
I hope this helps! Let me know if you have any other questions.
