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1. Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?
[Here, we have taken individual remainder such as 1421 divided by 12 gives remainder 5, 1423 and 1425 gives the remainder as 7 and 9 on dividing by 12.]
Now, the sum is reduced to,
= Remainder ⇒ -1 × -3 = 3 [Here, we have taken negative remainder.] So, required remainder will be 3.
Note: When, it gives positive remainder as 9 and it also give a negative remainder -3. As per our convenience,we can take any time positive or negative remainder.
Solution:
Remainder,[Here, we have taken individual remainder such as 1421 divided by 12 gives remainder 5, 1423 and 1425 gives the remainder as 7 and 9 on dividing by 12.]
Now, the sum is reduced to,
= Remainder ⇒ -1 × -3 = 3 [Here, we have taken negative remainder.] So, required remainder will be 3.
Note: When, it gives positive remainder as 9 and it also give a negative remainder -3. As per our convenience,we can take any time positive or negative remainder.