Question

The third number is the HCF of first two numbers What are the three numbers ?
A. 8, 60, 14
B. 40, 56, 8
C. 4, 20,5
D. 2, 3, 4​

Answer 1

$\textbf{Given:}$

$\textsf{Third number is the HCF of  first two numbers}$

$\textbf{To find:}$

$\textsf{The correct option from the following:}$

$\mathsf{A.\;8,60,14}$

$\mathsf{B.\;40,56,8}$

$\mathsf{C.\;4,20,5}$

$\mathsf{D.\;2,3,4}$

$\textbf{Solution:}$

$\textsf{Consider, the numbers 8 and 60}$

$\mathsf{8=2^3}$

$\mathsf{60=2^2{\times}3{\times}5}$

$\mathsf{Since\;2^2\;is\;common,\;HCF=4}$

$\textsf{Consider, the numbers 40 and 56}$

$\mathsf{40=2^3{\times}5}$

$\mathsf{56=2^3{\times}3{\times}7}$

$\mathsf{Since\;2^3\;is\;common,\;HCF=8}$

$\implies\mathsf{HCF\;of\;40\;and\;56\;is\;8}$

$\implies\boxed{\mathsf{Correct\;option\;is\;B}}$

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The third number is the HCF of first two numbers What are the three numbers

A. 8, 60, 14

B. 40, 56, 8

C. 4, 20,5

D. 2, 3, 4

CONCEPT TO BE IMPLEMENTED

1. HCF = Highest Common Factor

2. For a given set of numbers their HCF must divide each of the numbers

EVALUATION

CHECKING FOR OPTION : A

14 does not divide 8 and 60

So 14 cannot be HCF of 8 and 60

So this option is not correct

CHECKING FOR OPTION : B

8 does not divide 40 and 56

So 14 can be HCF of 40 and 56

More precisely

40 = 2 × 2 × 2 × 5

56 = 2 × 2 × 2 × 7

HCF = 2 × 2 × 2 = 8

So HCF of 40 and 56 = 8

So this option is correct

CHECKING FOR OPTION : C

4 does not divide 5

So 4 cannot be HCF of 20 and 5

So this option is not correct

CHECKING FOR OPTION : D

4 does not divide 2 and 3

So 4 cannot be HCF of 2 and 3

So this option is not correct

FINAL ANSWER

Hence the correct option is B. 40, 56, 8

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