Two positive numbers differ by 2134. When the greater number is divided by the smaller number, the quotient is 2 and the remainder is 147. What is the HCF of the greater of the two given numbers and 4225?​

Correct option is D

Given:

Two positive number differ by 2134 

Dividing greater number by smaller number gives 2 quotient and remainder 147

Formula Used:

Dividend = Divisor × Quotient + Remainder

Solution: 

Let the smaller number be x

Then the greater number = x + 2134

Also, $$\frac{x + 2134}{x}$$​ = 2 remainder 147

x + 2134 = 2x + 147

2134 - 147 = x

x = 1987

Greater number = x + 2134 = 1987 + 2134 = 4121

Now,

Using Euclidean Algorithm:

4225 - 4121 = 104  Now, HCF (4121, 104)

4121 ÷ 104 = 39  remainder 65

HCF(104, 65)

104 ÷ 65 = 1 remainder 39

HCF(65, 39)

65 ÷ 39 = 1 remainder 26

HCF(39, 26)

39 ÷ 26 = 1 remainder 13

HCF(26, 13)

26 ÷ 13 = 2 remainder 0

Thus, The HCF of the numbers are 13