Wednesday

October 1, 2014

October 1, 2014

Posted by **Sumare** on Tuesday, July 16, 2013 at 12:34am.

- Math -
**Bosnian**, Tuesday, July 16, 2013 at 12:46am2002 = 2 * 7 * 11 * 13

- Math -
**Sumare**, Tuesday, July 16, 2013 at 1:08amI meant what are the steps to finding the Answer.

- Math -
**MathMate**, Tuesday, July 16, 2013 at 8:13amFrom the knowledge of divisibility, we know that 2 is a factor (all even numbers).

That reduces

2002=2*1001

Again, the difference of sums of alternate digits equals zero (1+0)-(0+1)=0, so it is divisible by 11.

That makes

2002=2*11*91

We should (try to) know all prime factorization for numbers below 100, which in this case is 7*13=91.

This completes the prime factorization of 2002 to

2002=2*11*7*13

Rule for 7,11 and 13 for large numbers.

By the way,the given example is an excellent demonstration of another property:

If the number is grouped in 3 digits from the right, difference of alternate groups has the same mod as the number itself with respect to divisors 7,11 & 13.

For example to factorize 78169,

we know from divisibility rules that it is not divisible by 2,3,5,11.

Now form groups of 3 digits: 78 & 169.

Take the difference 169-78=91.

Since we know that 91 is divisible by 7 and 13 (but not 11), we conclude that 78169 is divisible by 7 and 13. The prime factorization is then:

78169=7*13*859

(note: 859 is prime).

**Answer this Question**

**Related Questions**

Math - How do I find the Prime Factorization for the number 2002?

math(help) - please answer this one question because im clueless lol!!! A number...

math last one help - sally drew a factor tree of a composite number and ended up...

math - my number is a multiple of 5, but doesnt end in 5, the prime ...

math - You can use the prime factorization of a number, written as the product ...

math - Which numbers between 40 and 49 have 2 and 3 in their prime factorization...

math - I have the same question as Sally: What is the prime factorization of 225...

Math - What is my number? Clue 1: My number is a multiple of 5, but it does not ...

Math - Plz help dont know how to do this question. Write number 68 as a product ...

math - what's the prime factorization of 293? what's the prime factorization of ...