# Apc.1.1.13 what is the prime factorization of 30,030

• MHB
• karush
In summary, the conversation discusses the prime factorization of 30,030, with the information given that 1,001 is the product of the primes 7, 11, and 13. The options a, b, and d do not have all the primes, and c can be eliminated through observation. Therefore, the correct answer is e) 2*3*5*7*11*13. Additional factors such as 3 and 10 are also taken into consideration.
karush
Gold Member
MHB
$\tiny{apc.1.1.13}$
The number 1,001 is the product of the primes 7, 11, and 13
Knowing this,
What is the prime factorization of 30,030?

a, ${3 \cdot 7\cdot 10\cdot 13}$
b. ${30\cdot 7\cdot 11\cdot 13}$
c. ${2 \cdot 5\cdot 7\cdot 11\cdot 13}$
d. ${3\cdot 7\cdot 10\cdot 11\cdot 13}$
e. ${2\cdot 3\cdot 5\cdot 7\cdot 11\cdot 13}$

Ok I never studied number theory so don't know theorems
but a b and d don't have all primes, by observation c won't make it
so that leaves e

I hope

Not bad. I'd say take a look at a couple of factors. It's clearly divisible by 3. It's also clearly divisible by 10 = 2 x 5, so you are left with e).

-Dan

You are told that "1001 is the product of the primes 7, 11, and 13" and 30030= 30(1001).
So 30030 is 30(7*11*13) and 30= 3(10)= 2*3*5. 30030= 2*3*5*7*11*13

ok weird i didn't see that

## What is the prime factorization of 30,030?

The prime factorization of 30,030 is 2 x 3 x 5 x 7 x 11 x 13.

## How can I find the prime factorization of 30,030?

To find the prime factorization of 30,030, you can use prime factorization methods such as the factor tree method or the division method.

## Why is it important to know the prime factorization of a number?

Knowing the prime factorization of a number can help in simplifying fractions, finding the greatest common factor, and solving problems in algebra and number theory.

## What is the difference between prime factorization and prime numbers?

Prime factorization is the process of breaking down a number into its prime factors, while prime numbers are numbers that are only divisible by 1 and itself.

## Can a number have more than one prime factorization?

No, a number can only have one unique prime factorization. This is because prime numbers are the building blocks of all other numbers, and they can only be multiplied in one way to get a specific number.

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