Question

There are $45$ policemen and $18$ police dogs for a searching operation. They are distributed into smaller groups such that each group has equal strength in terms of police officers and police dogs, i.e., identical groups. Find the maximum possible such groups.

• A. Eight
• B. Nine
• C. Twelve
• D. None of the above

Answer 1

The correct option is B Nine

$45$ policemen and $18$ police dogs are to be distributed into smaller groups such that each group's strength is equal.

We need to find out the greatest factor of $45$ that is also a factor of $18,i.e.,$ the GCD.

Using long division method,GCD $=9$

$\therefore 9$ identical groups can be formed.