SOLUTION: Consider m=2^9*17^3*67^2. Without elaborate calculation, tell which of the following expressions could not be factors of m. Explain how you know.
1.) 2^8*7
2.) 2^10*17^2*67
3.)
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-> SOLUTION: Consider m=2^9*17^3*67^2. Without elaborate calculation, tell which of the following expressions could not be factors of m. Explain how you know.
1.) 2^8*7
2.) 2^10*17^2*67
3.)
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Question 1192331: Consider m=2^9*17^3*67^2. Without elaborate calculation, tell which of the following expressions could not be factors of m. Explain how you know.
1.) 2^8*7
2.) 2^10*17^2*67
3.) 2^8*17^2*67^2
4.) 34^3
5.) 134^2 Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39617) (Show Source):
The given number (2^9)*(17^3)*(67^2) is shown in its prime factored form. Any number that is a factor of that number can have....
up to 9 factors of 2;
up to 3 factors of 17; and
up to 2 factors of 67;
and it can have no other prime factors.
Note when checking each of the possible factors, you need to write that factor in prime factored form.
(1) (2^8)(7) -- NO; the given number has no factors of 7
(2) (2^10)(17^2)(67) -- NO; the given number has only 9 factors of 2, not 10
(3) (2^8)(17^2)(67^2) -- YES; the given number has sufficiently many factors of 2, 17, and 67
(4) (34^3) = (2^3)(17^3) -- YES; the given number has sufficiently many factors of 2 and 17
(5) (134)^2 = (2^2)(67^2) -- YES; the given number has sufficiently many factors of 2 and 67
ANSWER: (1) and (2) can't be factors of the given number
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