Find the nearest integer to 5347 which is exactly divisible by 137.

First, divide 5347 by 137 to find the remainder:
5347÷137=39 with a remainder
Let us calculate the exact multiples of 137 close to 5347:

137×39=5343
137×40=5480
Now, find the distance from 5347 to these multiples:

Distance to 5343=∣5347−5343∣=4
Distance to 5480=∣5480−5347∣=133
Since 4<133, the nearest integer to 5347 exactly divisible by 137 is 5343.