IF 10 and 6 are factors of n, then 10 x 6 is a factor of n ... .

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IF 10 and 6 are factors of n, then 10 x 6 is a factor of n ... .

IF 10 and 6 are factors of n, then 10 x 6 is a factor of n..

What is one possible value for n between 1 and 100 that proves the statement above is false?
(The answer is \\\"30 or 90\\\".)
I can sense why the answer is so but don\\\'t know how to explain it.
Can you walk me through it?

Posted 196 day ago

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Answers (6)

asad.taj

answer is 60.
Tell me what is your supposition for the answers 30 and 60.

Posted 193 day ago

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atta	One value for n between 1 and 100 that proves that the above statement is false is mainly that of (n = 45) because 60 = n => 60f = n => f = 45/60 = 9 / 12 = 3 / 4. J.C Posted 194 day ago ( 0 ) ( 0 ) Report Abuse

math_fanatic

Another thing to consider is that 10 and 6 are not prime numbers so just because they are factors of some number n does not mean that their product will be a factor.

if you broke down the numbers into primes: 10 = 2*5 and 6 = 2*3, then 2*5*3 is a factor of n but NOT necessarily 2*5*2*3 although it COULD be depending on the number. It is not required for n to have an additional prime factor of 2 in order for both 10 and 6 to be factors but it would be required in order for 10*6 to be a factor of n.

The prime factorization of 60 is 2*2*3*5 and the prime factorization of 120 is 2*2*2*3*5.
Both have 6 and 10 as a factor because there are enough 2's to generate them.

The prime factorization of 90 however is 2*3*3*5 so both 10 and 6 are factors but there are not enough 2's present to make 6*10 a factor which again is 2*2*3*5

Any other number that possesses the prime factors 2,2,3,5 will also have the factor 6 * 10 or 60.

I hope that makes sense.

Posted 196 day ago

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matherapist

The only thing i would add to the answer is that 6 and 10 are factors of 30 and 90.

Posted 196 day ago

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Hi, this is rajbaba78. If you are satisfied with my answer, I will appreciate if you inform me. Thak you.

Posted 196 day ago

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if 6 and 10 are factors of n, then for 6x10 = 60 to be a factor of n, n must be either 60, or 120, or 180 or 60t where t = 1,2,3,...etc
Now, for n between 1 to 100, neither 30 nor 90 would satisfy the required condition.

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