QuestionFind the prime factors of the number 105. What is its prime factorization?
Studdy Solution
STEP 1
Assumptions1. The number given is105. We need to find the prime factorization of this number3. A prime factorization of a number is the expression of that number as a product of prime numbers
STEP 2
To find the prime factorization of a number, we start by dividing the number by the smallest prime number, which is2. If the number is not divisible by2, we move to the next prime number, which is, and so on.
STEP 3
Check if105 is divisible by2.
STEP 4
105 is not divisible by2 (since it's an odd number), so we move to the next prime number, which is3.
STEP 5
Check if105 is divisible by3.
STEP 6
105 is divisible by3. So, we divide105 by3.
STEP 7
Now, we continue the process with the quotient,35. Check if35 is divisible by2.
STEP 8
35 is not divisible by2 (since it's an odd number), so we move to the next prime number, which is3.
STEP 9
Check if35 is divisible by3.
STEP 10
35 is not divisible by3, so we move to the next prime number, which is5.
STEP 11
Check if35 is divisible by5.
STEP 12
35 is divisible by5. So, we divide35 by5.
STEP 13
Now, we continue the process with the quotient,7. Check if7 is divisible by2.
STEP 14
7 is not divisible by2 (since it's a prime number), so we move to the next prime number, which is3.
STEP 15
Check if7 is divisible by3.
STEP 16
is not divisible by3, so we move to the next prime number, which is5.
STEP 17
Check if7 is divisible by5.
STEP 18
7 is not divisible by5, so we move to the next prime number, which is7.
STEP 19
Check if7 is divisible by7.
STEP 20
7 is divisible by7. So, we divide7 by7.
STEP 21
Now, we have reached1, which means we have found all the prime factors of105.
STEP 22
The prime factorization of105 is the product of the prime numbers we used to divide, which are,5, and7.
The prime factorization of105 is .
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