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Write 2730 as a product of prime factors.
Enter your answer as a product of prime numbers, like
2×3, or as a single prime number, like 17.

Write $2730$ as a product of prime factors. $\newline$ Enter your answer as a product of prime numbers, like $\newline$ $2\times3$ , or as a single prime number, like $17$ .

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Find the sum of a finite geometric series

Full solution

Q. Write

2730

as a product of prime factors.

\newline

Enter your answer as a product of prime numbers, like

\newline

2\times3

, or as a single prime number, like

17

.

Find Smallest Prime Number: Begin by finding the smallest prime number that divides $2730$ . The smallest prime number is $2$ . Check if $2730$ is divisible by $2$ . $2730 \div 2 = 1365$ Since $1365$ is a whole number, $2$ is a prime factor of $2730$ .
Continue Factoring Quotient: Continue factoring the quotient $1365$ by the smallest prime numbers. $\newline$ The next smallest prime number after $2$ is $3$ . Check if $1365$ is divisible by $3$ . $\newline$ $1365 \div 3 = 455$ $\newline$ Since $455$ is a whole number, $3$ is a prime factor of $1365$ .
Factor Quotient by Prime Numbers: Factor the quotient $455$ by the smallest prime numbers. $\newline$ $455$ is not even, so we test if it's divisible by $3$ . $\newline$ $455 \div 3$ is not a whole number, so we try the next prime number, which is $5$ . $\newline$ $455 \div 5 = 91$ $\newline$ Since $91$ is a whole number, $5$ is a prime factor of $455$ .
Factor Quotient by Prime Numbers: Factor the quotient $91$ by the smallest prime numbers. $\newline$ $91$ is not even, and it is not divisible by $3$ or $5$ . The next prime number is $7$ . $\newline$ $91 \div 7 = 13$ $\newline$ Since $13$ is a whole number and also a prime number, $7$ and $13$ are prime factors of $91$ .
Write as Product of Prime Factors: Write $2730$ as a product of the prime factors we have found. $2730 = 2 \times 3 \times 5 \times 7 \times 13$

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