find the prime factorization of 175
Start with 5.
175/5 = 35
Now factor 5 and 35
175 answer of prime factiostin
To find the prime factorization of 175, we need to find the prime numbers that multiply together to give us 175.
We can start by dividing 175 by the smallest prime number, which is 2.
175 ÷ 2 = 87 remainder 1
Since 2 does not evenly divide into 175, we move on to the next prime number, which is 3.
175 ÷ 3 = 58 remainder 1
Again, 3 does not evenly divide into 58, so we move on to the next prime number, which is 5.
175 ÷ 5 = 35
Finally, we have found a prime factor of 175.
So the prime factorization of 175 is 5 × 5 × 7, or 5² × 7.
To find the prime factorization of 175, you need to determine the prime numbers that can divide the number evenly. Here's how you can find the prime factorization of 175:
Step 1: Start by dividing the number by the smallest prime number, which is 2. However, 175 is an odd number and not divisible by 2, so we move to the next prime number.
Step 2: Divide 175 by the next prime number, which is 3. By performing the division, we get that 175 ÷ 3 = 58 remainder 1.
Step 3: Since we didn't get an even result in the previous step, we continue by dividing the quotient (58) by the next prime number, which is 5. We find that 58 ÷ 5 = 11 remainder 3.
Step 4: Again, we have a remainder, so we proceed to divide 11 by the next prime number, which is 7. We get 11 ÷ 7 = 1 remainder 4.
Step 5: Finally, we try to divide the remaining quotient (1) by 11, the last prime number we have. The division gives us 1 ÷ 11 = 0 remainder 1.
Step 6: At this point, the quotient is 0, so we have found the prime factorization of 175. It can be expressed as 175 = 5 × 5 × 7.
Therefore, the prime factorization of 175 is 5 × 5 × 7, or written in exponent form: 175 = 5² × 7.