Question

find the largest possible positive integer that will divide 125, 162 and 259 leaving reminder 5,6 and 7 respectively<br />A.6<br />B.8<br />C.12 <br />D.13

Answer 1

Hi there!
Here's the answer:

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¶¶¶ TYPE OF PROBLEM :
The largest possible positive integer that will divide x, y and z leaving reminder a, b and c respectively


¶¶¶ APPROACH TO PROBLEM:
• Find (x-a), (y-b).& (z-c)
• Find the HCF of the above three No.s gives the required largest possible integer.

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¶¶¶ SOLUTION:

Given,

x = 125 ; y = 162 ; z = 259
a = 5 ; b = 6 ; c = 7

x-a = 125 - 5 = 120
y-b = 162 - 6 = 156
z-c = 259 - 7 = 252


•Using prime factorisation, resolving the No.s into prime factors and expressing the the No. as product of prime factors in exponential form

120 = 2×2×2×3×5 = 2³ × 3 × 5
156 = 2×2×3×13 = 2² × 3 × 13
252 = 2×2×3×3×7 = 2² × 3² × 7

•Now find HCF

clearly, HCF = 2² × 3 = 4 × 3 = 12


•°• Required Largest Integer = 12


This Option exists in Option C
•°• Option C is the correct Choice

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