Answer :
Sure! Let’s factor each number into its prime components.
i) Factorize 157:
157 is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, the prime factorization of 157 is simply 157.
Prime factorization of 157: [tex]\( 157 \)[/tex]
ii) Factorize 40:
To factorize 40, we start by dividing it by the smallest prime number, which is 2, and continue dividing by prime numbers until we reach 1.
1. 40 is even, so divide by 2:
[tex]\[
40 \div 2 = 20
\][/tex]
2. 20 is even, so divide by 2 again:
[tex]\[
20 \div 2 = 10
\][/tex]
3. 10 is even, so divide by 2 once more:
[tex]\[
10 \div 2 = 5
\][/tex]
4. 5 is a prime number.
Now, we've broken 40 down completely into prime factors:
Prime factorization of 40: [tex]\( 2 \times 2 \times 2 \times 5 \)[/tex], which can also be written as [tex]\( 2^3 \times 5 \)[/tex].
These are the prime factorizations of the given numbers.
i) Factorize 157:
157 is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, the prime factorization of 157 is simply 157.
Prime factorization of 157: [tex]\( 157 \)[/tex]
ii) Factorize 40:
To factorize 40, we start by dividing it by the smallest prime number, which is 2, and continue dividing by prime numbers until we reach 1.
1. 40 is even, so divide by 2:
[tex]\[
40 \div 2 = 20
\][/tex]
2. 20 is even, so divide by 2 again:
[tex]\[
20 \div 2 = 10
\][/tex]
3. 10 is even, so divide by 2 once more:
[tex]\[
10 \div 2 = 5
\][/tex]
4. 5 is a prime number.
Now, we've broken 40 down completely into prime factors:
Prime factorization of 40: [tex]\( 2 \times 2 \times 2 \times 5 \)[/tex], which can also be written as [tex]\( 2^3 \times 5 \)[/tex].
These are the prime factorizations of the given numbers.
