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Answer :
Sure! Let's find the prime factorization of 220 step by step.
1. Start with the smallest prime number:
- 220 is an even number, so we can divide it by 2:
[tex]\[
220 \div 2 = 110
\][/tex]
- So, one of the prime factors is 2.
2. Continue with the quotient (110):
- 110 is also even, so we can divide by 2 again:
[tex]\[
110 \div 2 = 55
\][/tex]
- Thus, we have another prime factor of 2.
3. Move to the next prime number:
- 55 is not divisible by 2, so we try the next smallest prime number, 3, but 55 is not divisible by 3 either.
- Next, we try 5, which is a factor of 55:
[tex]\[
55 \div 5 = 11
\][/tex]
- So, we have a prime factor of 5.
4. Check the quotient (11):
- 11 is a prime number itself and cannot be divided further except by 1 or 11.
Now we have all the prime factors. The prime factorization of 220 is:
[tex]\[
220 = 2 \times 2 \times 5 \times 11
\][/tex]
This means that the prime factors of 220 are [tex]\( 2^2 \)[/tex], 5, and 11.
1. Start with the smallest prime number:
- 220 is an even number, so we can divide it by 2:
[tex]\[
220 \div 2 = 110
\][/tex]
- So, one of the prime factors is 2.
2. Continue with the quotient (110):
- 110 is also even, so we can divide by 2 again:
[tex]\[
110 \div 2 = 55
\][/tex]
- Thus, we have another prime factor of 2.
3. Move to the next prime number:
- 55 is not divisible by 2, so we try the next smallest prime number, 3, but 55 is not divisible by 3 either.
- Next, we try 5, which is a factor of 55:
[tex]\[
55 \div 5 = 11
\][/tex]
- So, we have a prime factor of 5.
4. Check the quotient (11):
- 11 is a prime number itself and cannot be divided further except by 1 or 11.
Now we have all the prime factors. The prime factorization of 220 is:
[tex]\[
220 = 2 \times 2 \times 5 \times 11
\][/tex]
This means that the prime factors of 220 are [tex]\( 2^2 \)[/tex], 5, and 11.
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