explain why 5 x 4 x 3 x 2 x 1 + 3 is a composite number?

Question

explain why 5 x 4 x 3 x 2 x 1 + 3 is a composite number?

 

Answer 1

you can do the arithmetic and look at the result...

5x4x3x2x1+3=120+3=123

123 is divisible by 1, 123, and also by 3 because 1+2+3=6 and 6 is divisible by 3 (rule for divisibility by 3)

also, if 123 is divisible by 3, then 123/3=41

the factors of 123 are 1, 3, 41, and 123, therefore 123 is composite because it has more than 2 different whole number factors

another way to look at this...

5x4x3x2x1+3=3x(5x4x2x1)+3=3x40+3x1

now factor out the 3

3x(40+1)=3x41

therefore the expression written is divisible by 1 (trivial case), divisible by 3, divisible by 41, and divisible by its value which is 123 (trivial case again)  (a whole number is divisible by 1 and divisible by itself, so if there are more factors, the number is a composite number)