The number 1,001 is the product of the prime numbers 7, 11, and 13. Knowing this, what is the prime factorization of 30,030?

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Answer 1 · 2018-08-08T12:21:53

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Because the number ends in an even number the first prime number we can factor out of 30,030 is 2:

#30030 = 2 xx 15015#

Because the 15015 ends in a 5 the next prime number we can factor out of 30,030 is 5:

#30030 = 2 xx 5 xx 3003#

Because the 3003 is divisible by 3 the next prime number we can factor out of 30,030 is 3:

#30030 = 2 xx 3 xx 5 xx 1001#

From the problem we know the prime factors of 1001 are 7 11 and 13 which gives is:

#30030 = 2 xx 3 xx 5 xx 7 xx 11 xx 13#