Answer:
[tex]a=8,b=2,c=3[/tex]
Step-by-step explanation:
Given:
[tex]40=16+24=a(b+c)[/tex]
Now, in order to write 16 + 24 into a product of two numbers, we need to find the factors of 16 and 24.
Factors of 16 = 1, 2, 4, 8, 16.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Now, common factors for 16 and 24 are 1, 2, 4 and 8.
Now, the values of [tex]b\textrm{ and }c[/tex] should be such that there should be no common factors between them except 1. In other words, [tex]b\textrm{ and }c[/tex] are prime numbers.
So, in order to get prime numbers for [tex]b\textrm{ and }c[/tex], we should take the greatest common factor for 16 and 24 which is 8.
Therefore 40 = 16 + 24 can rewritten as:
[tex]16+24=8(2+3)[/tex]
So, [tex]a=8,b=2,c=3[/tex]
