The $H . C . F$ of $9 / 10, 12 / 25, 18 / 35, 21 / 40$ is:

3 / 5

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252 / 5

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3 / 1400

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63 / 700

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Solution

The correct option is C $3 / 1400$
H.C.F of fractions $= \frac{H . C . F o f n u m e r a t o r}{L . C . M o f d e n o m i n a t o r}$
$= \frac{H . C . F (9, 12, 18, 21)}{L . C . M (10, 25, 35, 40)}$
Factors of $9 = 3 \times 3$
Factors of $12 = 3 \times 2 \times 2$
Factors of $18 = 3 \times 3 \times 2$
Factors of $21 = 3 \times 7$
Common factor $= 3$
$∴$ H.C.F $= 3$
Factors of $10 = 5 \times 2$
Factors of $25 = 5 \times 5$
Factors of $35 = 5 \times 7$
Factors of $40 = 5 \times 2 \times 2 \times 2$
L.C.M $= 1400$
H.C.F $= \frac{3}{1400}$

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