What number has the prime factorization $2^3 \times 5^2 \times 7$ ? How did you find the number?

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What number has the prime factorization $2^3 \times 5^2 \times 7$ ? How did you find the number?

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Answer 1 · 2018-03-07T07:34:35

$1400$

Explanation:

Given: prime factorization $2^3 xx 5^2 xx 7$

$2^3 xx 5^2 xx 7 = 2 xx 2 xx 2 xx 5 xx 5 xx 7$

$= 8 xx 25 xx 7 = 200 xx 7 = 1400$

Answer 2 · 2018-03-07T07:55:59

$2^3×5^2×7$ equals $1400$

Explanation:

$2^3×5^2×7$ equals what number?

You find the number by multiplying all its factors together.

$2^3 × 5^2 ×7$

$color(white)(.)$ $8 × 25 × 7$

$color(white)(.)$ ╲ ╱ $darr$

$color(white)(.)$ $200 xx 7$

$color(white)(......)$ ╲ ╱

$color(white)(......)$ 1400

$color(white)(............)$ ――――――

Check

Factor $1400$ into its prime factors and see if that brings back the same factors that were in the original question.

$color(white)(......)$ 1400

$color(white)(......)$ ╱ ╲

$color(white)(m)$ $14 xx 100$

$color(white)(m)$ ╱ ╲ ╱ ╲

$color(white)()$ $2 xx 7 xx 2 xx 50$

$darr$ $darr$ $darr$ ╱ ╲

$color(white)(.)$ $2 xx7 xx 2 xx 2 xx 25$

$darr$ $darr$ $darr$ $darr$ ╱ ╲

$color(white)(.)$ $2 xx7 xx 2 xx 2 xx 5 xx 5$

$2^3 xx 5^2 xx 7$

$Check$

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What number has the prime factorization $2^3 \times 5^2 \times 7$ ? How did you find the number?

2 Answers

Explanation:

Explanation:

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What number has the prime factorization $2^3 \times 5^2 \times 7$ ? How did you find the number?