what is the prime factorization of 175
The prime factorization of 175 is 5 x 5 x 7 or 5² x 7.
To find the prime factorization of 175, we need to find the prime numbers that divide 175 evenly.
Step 1: Start by dividing 175 by the smallest prime number, which is 2. However, 2 does not evenly divide 175.
Step 2: Next, try dividing 175 by the next prime number, which is 3. 175 divided by 3 is not a whole number, so it is not divisible by 3.
Step 3: Now, divide 175 by the next prime number, which is 5. 175 divided by 5 is equal to 35.
Step 4: We have found one prime factor, which is 5. Now we need to find the prime factors of the quotient, which is 35.
Step 5: Divide 35 by the smallest prime number, which is 2. However, 2 does not evenly divide 35.
Step 6: Next, try dividing 35 by the next prime number, which is 3. 35 divided by 3 is not a whole number, so it is not divisible by 3.
Step 7: Divide 35 by 5. 35 divided by 5 is equal to 7.
Step 8: We have found another prime factor, which is 5. Now we need to find the prime factors of the quotient, which is 7.
Step 9: Divide 7 by the smallest prime number, which is 2. However, 2 does not evenly divide 7.
Step 10: Divide 7 by 3. 7 divided by 3 is not a whole number.
Step 11: Divide 7 by 5. 7 divided by 5 is not a whole number.
Step 12: Since 7 cannot be divided any further, we have found the prime factorization of 175, which is 5 x 5 x 7, or written as 5^2 x 7.
To find the prime factorization of 175, we will first divide it by the smallest prime number, which is 2. However, since 175 is an odd number and not divisible by 2, we move on to the next prime number, which is 3.
When we divide 175 by 3, we get 58 remainder 1. This means that 3 is not a factor of 175.
Next, we move on to the next prime number, which is 5. When we divide 175 by 5, we get 35 with no remainder. This means that 5 is a factor of 175, and the result of this division is a smaller composite number that needs to be further factorized.
Now, we can divide this new number, 35, by the smallest prime number, 2. However, since 35 is odd and not divisible by 2, we move on to the next prime number, which is 3.
When we divide 35 by 3, we get 11 with no remainder. This means that 3 is not a factor of 35.
Since 11 is a prime number, we have found the prime factorization of 175: 5 × 5 × 7.
Therefore, the prime factorization of 175 is 5^2 × 7.