What is the prime factorization of 42 using continuous division?

Answer 1

Using the division method to find prime factors

1. let x be the number to be factorised
2. let p be the first Prime number below the square root of x (always 2, unless x is below 4)
3. Calculate x/p
4. if x/p was an integer, update the list of factors to include p and let x = x/p
5. if x > 1, return to step 3
6. you now have your completed list

Answer 2

Start by dividing by the smallest prime number which evenly 'goes into' the given number. Look at that answer and do the same, divide by the smallest prime number which evenly 'goes into' it. Continue until the last answer is prime.

ALL these numbers that you have divided by and that last prime number answer = the prime factorization of the original.

EX: find the prime factorization of 170.

170 is even, so divide by 2 ..... 170 / 2 = 85

85 is not even don't use 2 again) and is not divisible by 3, but it is div. by 5

so .... 85 / 5 = 17

17 is prime. Now collect the prime factors for the answer.

We divided by 2 first and then 5 and this left us with 17 as the last prime.

170 = 2 x 5 x 17 this is the answer

sometimes you must divide by the same prime several times so it will appear in the prime factorization more than once.

Try 300 and you can see that the prime factorization will be

2 x 2 x 3 x 5 x 5

because you can't use 4 or 25 since they are not prime.

Answer 3

42/2 = 21/3 = 7/7 = 1

2 x 3 x 7 = 42

Answer 4

24/2 = 12/2 = 6/2 = 3/3 = 1

2 x 2 x 2 x 3 = 24