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Two ways: Find the square root first. If it's a whole number, find the prime factorization like you would for any other number. Or, find the prime factorization of the original number. The factors will be paired. Take one out of of each pair.
Example: 900
The square root of 900 is 30.
The prime factorization of 30 is 2 x 3 x 5
or
The prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5
The square root will be 2 x 3 x 5, or 30
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What is the prime factorization of the square root of 99856?
The prime factorisation of the square root of 99856 is 2*2*79.
How do you get the prime factorization of 90?
Prime Factorization of 90To find the prime factorization of 90, start with the lowest prime number that will divide into 90. That number is 2. 2 times 45 equals 90. 2 is a number in the prime factorization of 90. Next, find the lowest prime number that will divide into 45. The number is 3, and 3 times15 equals 45. 3 is one of the prime factors, so now you have 2 times 3 times 15. 15 is not a prime number, and the lowest prime number that will divide into 15. 3 times 5 is 15. You'll notice that both 3 and 5 are prime numbers, so the prime factorization of 90 is 2 X 3 X 3 X 5. Check your answer to make sure it is correct and you're done.
What is the square root of 256 evaluated using prime factorization?
The prime factorization of 256 is 28. The square root is 24 or 16.
What is the prime factorization of 1369?
37 x 37 = 1369 The square root is 37.
Is there a prime factor greater than the square root of an integer?
No there is not. If you are looking for prime factors of a number and you get to the square root of that number you can stop. Yes, there is. If an integer is not itself a prime, then one of its factors will be less or equal to its square root and the "co-factor" will be greater than or equal to the square root. But both cannot be greater than the square root so, when searching for factors, you can stop when you reach the square root.
