Question

Hcf of two numbers obtained in three steps of division is 7 and the first 3 quotient are 2,4 and 6 respectively.the numbers are

Please answer with steps

Answer 1

A/C to question,

HCF of two numbers obtained in three steps of division is 7. so, divisor and remainder in the 3rd step are 7 and 0 respectively.

also quotient in the 3rd step is 6.

from Euclid division lemma ,

dividend = divisor × quotient + remainder

dividend in the 3rd step = 6 × 7 + 0 = 42

so, divisor in the 2nd step = 42

quotient in the 2nd step = 4

remainder in the 2nd step = 7

so, dividend in the 2nd step = 42 × 4 + 7 = 175

so, divisor in the 1st step = 175

hence, one number is 175

quotient in the 1st step = 2

remainder in the 1st step = 42

so, dividend in the 1st step = 175 × 2 + 42 = 392

hence, 2nd number is 392.

therefore 175 and 392 are two unknown numbers .