What are the divisors of 3?

Number Theory Level 1

If 3 X \frac 3X is an integer, then which of the following must be an integer as well?

4 X \frac4X 5 X \frac5X 6 X \frac6X

Pi Han Goh by Pi Han Goh , 30, Malaysia

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4 solutions

Marta Reece
Jul 30, 2017

6 X = 2 × 3 X \frac6X=2\times\frac3X

Multiplying an integer by 2 2 produces an integer.

The other numerators are not multiples of 3 3 and so those numbers need not be integers.

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Feb 9, 2018

3 x × 2 = 6 x \frac{3}{x} \times 2=\frac{6}{x}

so, 6 x \frac{6}{x} must be an integer.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Noel Lo
Jul 31, 2018

6 X = 2 × 3 X = 2 ( 3 X ) \dfrac{6}{X}=\dfrac{2\times3}{X}=2\left(\dfrac{3}{X}\right)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

In this problem, x x must be a multiple of 3 3 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Wrong. 9 is a multiple of 3, but 3/9 is not an integer.

What you're looking for is the word "factor / divisor," not "multiple."

Pi Han Goh - 3 years, 10 months ago

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