Question

Show that 13X31X41X63+41 is a composite Number.
Show that 3X4X12+24 is a composite number.
Check whether 5 can end with the Digit 0 for any n ∈ N.
Find the smallest number which when divided by 39,52and91 leaves a
remainder 13 in each case?

Answer 1

Answer:

take 41 common in first expression.

(13×31×63+1)×41

that is product of two numbers.

hence composite

Answer 2

Answer:

a) Proved

b) Proved

c) Proved

d) 1,84,561

Step-by-step explanation:

a) A composite number is a number which has more than one factors excluding itself and 1. Here the given number is a composite number as it contains 31 , 41 and 13 which are prime factors and adding 41 to it creates a new factor 2.

b) Similarly here we have 3 , 2 as factors hence it is composite.

c) 5 cannot end with 0 for ant integer n as 5 is not divisible by 2. As we know a number can have the digit 0 at the end if and only if is divisible by 2 and 5.

d) First we need to find product of the three number 39 , 52 and 91.

Product = 1,84,548

So by Euclid's theorem,

$a =bq+r$

a = 184548 + 13 = 1,84,561

Euclid's theorem

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