How many pairs of whole numbers have a sum of 40?

21 pairs

A whole number is one of the numbers set {0, 1, 2, 3, 4, ...}. They are a set of positive integers along with zero and don't include the fraction or decimal numbers.

We determine how many pairs of whole numbers have a sum of 40. Let us notice below.

Hence, there are 21 pairs.

The next setting is a repeat pair. Remember, because the order in pairs does not have an effect so that , vice versa. Exactly like this:

(21, 19) ⇔ (19, 21), (22, 18) ⇔ (18, 22)

and so forth, until (39, 1) ⇔ (1, 39), (40, 0) ⇔ (0, 40)

Note, we can use the principle of finding many terms from the arithmetic sequence, even though they are not too many.

The general term of an arithmetic sequence (aₙ) with common difference d is

Given:

How many terms (n)?

We get , i.e., whole numbers pairs that have a number of 40.

A complete description of natural numbers, whole numbers, and integers can be explored at link.

Keywords: whole numbers, how many pairs, a sum of 40, exact, positive numbers, integers, natural, arithmetic sequence

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18