A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively ?

A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively ? Correct Answer 45 and 76

Cows = 945, Sheep = 2475
⇒ For largest flocks take HCF
$$ \Rightarrow \underbrace {945\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{2475}}}_{ - 1530}$$
⇒ For HCF take difference of number HCF will either be the difference or its factors
⇒ 1530
= 17 × 3 × 3 × 5 × 2
= 17 × 2 × 45
HCF = 45
∴ Maximum animals in each flock = 45
∴ Number of folks of cows are
$${\text{ = }}\frac{{945}}{{45}} = 21$$
∴ Number of folks of sheep are
$${\text{ = }}\frac{{2475}}{{45}} = 55$$
Total number of flocks
= 21 + 55 = 76 (45, 76)