Answer Hint: When the required number divides the given numbers (285 and 1249), it leaves certain remainders, thus the difference between the two will provide us those numbers that are completely divisible by the required number. Complete step-by-step answer: As we have to find the greatest number that divides the two, we need to highest common factor (H.C.F) of the two numbers obtained after subtraction.The numbers are given by the difference exactly divisible by the required number are given as:285 – 9 = 2761249 – 7 = 1242To find the greatest number that exactly divides these are given by their H.C.F:276 = 2 X 2 X 3 X 231242 = 2 X 3 X 3 X 3 X 23Common numbers = 2 X 3 X 23Highest Common Factor (H.C.F) = 6 X 23Highest Common Factor (H.C.F) = 138Therefore, the greatest number which divides 285 and 1249 leaving the remainder 9 and 7 respectively is 138, option D).So, the correct answer is “Option D”. Note: A factor is a number that divides another number without leaving any remainder.
TCS Programming and Technical Numerical Ability LCM and HCF
Find the greatest number that will divide 148 246 and 623 leaving remainders 4 6 and 11 respectively ? Remainder in case of 148 = 4 Number = 148 – 4 = 144 Remainder in case of 246 = 6 Number = 246 – 6 = 240 Remainder in case of 623 = 11 Number = 623 – 11 = 612 Now, we have find the H.C.F. of 144, 240 and 612 H.C.F. of 144, 240 and 612 = 2 * 2 * 3 = 12 Therefore, the required number is 12 that will divide 148, 246 and 623 leaving remainders 4, 6 and 11 respectively. |