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Answer :
The prime factorization of 187 is expressed as: [tex]187 = 11 \times 17[/tex].
To find the prime factorization of 187, follow these steps:
1. Understanding Prime Factorization:
- Prime factorization is the process of expressing a number as the product of its prime factors.
- Prime numbers are numbers greater than 1 that cannot be divided evenly by any other numbers except for 1 and themselves.
2. Start Dividing:
- Begin by testing the smallest prime numbers to see if they can divide 187 evenly.
- Start with 2 (the smallest prime number).
Since 187 is odd, we skip it.
- Next, try 3.
Add the digits of 187: 1 + 8 + 7 = 16.
Since 16 is not divisible by 3, 187 is not divisible by 3.
- Move to 5.
The last digit of 187 is not 0 or 5, so it's not divisible by 5.
- Now, try 7.
Performing the division: 187 ÷ 7 = 26.71
- Next is 11.
Dividing: 187 ÷ 11 = 17 (exactly, since 11 x 17 = 187).
3. Identifying Prime Factors:
- The numbers identified in the division are 11 and 17. Both are prime numbers.
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