How do I find the Prime Factorization for the number 2002?
divide by larger and larger primes till you get a quotient of 1.
2002/2 = 1001
2 does not divide 1001
3,5 do not divide 1001
1001/7 = 143
7 does not divide 143
143/11 = 13
11 does not divide 13
13/13 = 1
So, 2002 = 2x7x11x13
http://www.mathwarehouse.com/arithmetic/numbers/prime-number/prime-factorization.php?number=2002#primeFactorization
To find the prime factorization of a number, like 2002, you need to factorize it into its prime factors. Here's how you can find the prime factorization of 2002:
1. Start by dividing the number by the smallest prime number, which is 2.
2002 ÷ 2 = 1001
2. Since 1001 is not divisible by 2 anymore, move on to the next prime number, which is 3.
1001 ÷ 3 = 333
3. Continue dividing by the smallest prime numbers until you can no longer find a small prime factor.
333 ÷ 3 = 111
4. Now, divide by 111 by the next prime number, which is 11.
111 ÷ 11 = 10
5. Finally, as 10 is divisible by 2, divide by 2 one more time.
10 ÷ 2 = 5
Since 5 is a prime number, we have completed the prime factorization.
So, the prime factorization of 2002 is: 2 × 3 × 3 × 11 × 5, or in exponential form: 2^1 × 3^2 × 11^1 × 5^1.