prime factorisation method of
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Answer:
The QUESTION IS INCOMPLETE
NO WORRIES I HV GIVEN HERE RELATEDLY
Step-by-step explanation:
Examples of Prime Numbers:
The number 2 is a prime number because it is divisible only by 1 and 2 (itself)
The number 17 is a prime number because it has exactly two factors which are 1 and 17 (itself)
The number 31 is a prime number because it can only be divided by two numbers namely 1 and 31 (itself)
Examples of Numbers that are Not Prime:
The number 10 is not a prime number because it is divisible by 1, 5, and 10 (itself) therefore having more than two factors
The number 27 is not a prime number because it is divisible by more than two factors other than 1 and itself that includes 3 and 9
The number 49 is not a prime number because it can also be divided by 7 other than 1 and 49 (itself), thus having more than two factors
Now, I will explain the general steps involved in performing prime factorization of a given positive integer.
How to Perform Prime Factorization
Step 1: List down at least the first few prime numbers in increasing order. I will stop at 19 because this is large enough for the numbers in this tutorial that we will factorize.
2, 3, 5, 7, 11, 13, 17, 19 …
Step 2: For any given number, test if it is divisible by the smallest prime number which is 2. If the prime number 2 divides the given number evenly, then express it as factors:
the given number is equal to 2 times another number; where the given number is the number we start with, two (2) is the smallest prime number, and another number is the whole number that comes out after dividing by 2. we can also write this as given number = (2)(another number).
Step 3: Check again if the other number that comes out is divisible by 2. If it is, keep going until the new number is no longer divisible by 2. Two things can happen here:
After the repeated division of 2, you end up getting a prime number. Proceed to the final step. You’re almost done!
After the repeated division of 2, you end up having a composite number (not prime) but cannot be divided by 2. Move to Step 4.
Step 4: Move to the next larger prime numbers such as 3, 5, 7 and so on, as needed to check if the number that we left off in prior step can be divided evenly further. This repetitive process of dividing by prime numbers in increasing order will ultimately give us the last prime factor.
Final Step: At this point, we should have a long list of prime numbers that are being multiplied together. We just need to present our final answer as a product of exponential expressions with prime bases. That is it! A quick example may look like this…
the prime factorization of 72 is equal to 2 times 2 times 2 times 3 times 3. since the prime number 2 occurs three times and the prime number 3 occurs two times as factors, we can write the factors 2 and 3 in exponential form which are 2^3 and 3^2, respectively. we can also write this as, 72 = 2×2×2×3×3 = (2^3) × (3^2).
The exponent of each prime number tells how many times that prime occurs as factors.
