Foundation
Mathematics Foundation
HCF and LCM
Properties of Real Number
Remainder Theorem
Question
The greatest integer that divides 358,376 and 232. The same remainder in each case is
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Solution
If the remainder is the same in each case and the remainder is not given, HCF of the differences of the numbers is the required greatest number
Given: The greatest number that will divide 358,376 and 232 leaving the same remainder in each case.
To find: The number?
Solution :
First, we find the difference between these numbers.
The required numbers are
376 - 232 = 144
376 - 358= 18
358 - 232 = 126
Now, We find the HCF of 18, 126, and 144
18 = 2 × 32
126 = 2 × 32 × 7
144 = 24 × 32
HCF(18,126,144) = 2 × 3 × 3
Therefore, The required largest number is 18.