But is it a right approach to calculate GCF of 21 and 91 (which is 7) and therefore in my opinion also the greatest number of identical buquets? Or just by coincidence the same result? Answers appreciated!
It is not a coincidence.
To understand this, let's assume that we make n identical bouquets, in each of which:
Number of white flowers = w
Number of red flowers = r
Since we are given that no flower is to be left out, we can write:
wn = 21
And, rn = 91
That is, w = 21/n
And, r = 91/n
Now, w and r, being the number of flowers, have to be integers (because we cannot have 2.5 or 3.3 flowers in a bouquet)
So, n has to be a number that completely divides 21 as well as 91.
But the question asks us to find the greatest possible value of n.
That is, the greatest possible number that completely divides 21 as well as 91.
What is this number known as? Greatest Common Factor
Hope this helped clarify your doubt.