Find the greatest number that will divide 43, 91 and 183 leaving the same remainder in each case

To find the greatest number that will divide x, y and z leaving the same remainder in each case. (A) When the value of remainder r is given: Required number = H.C.F. of (x – r), (y – r) and (z – r). (B) When the value of remainder is not given:

Required number = H.C.F. of |(x – y)|, |(y – z)| and |(z – x)|

Question 16 Real Numbers Exercise 1B

Next

Answer:

The given numbers are 43, 91, and 183.

Subtract smallest number from both the highest numbers.

we have three cases:

183 > 43; 183 > 91 and 91 > 43

183 - 43 = 140

183 - 91 = 92 and

91 - 43 = 48

Now, we have three new numbers: 140, 48 and 92.

Find HCF of 140, 48, and 92 using the prime factorization method, we get

HCF (140, 48 and 92) = 4

The highest number that divides 183, 91, and 43 and leaves the same remainder is 4.

Was This helpful?