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

2 Answers
Mar 7, 2018

#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#

Mar 7, 2018

#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#