UPSC CAPF Assistant Commandant Model Paper 2

GIVEN:
[34×65×82×105×126×2512×208×1016×1520] is divisible by 10n
CONCEPT:
10 = 2 × 5
Whenever the expression is divisible by 10, there must have a pair of ‘2 and 5’ in the expression.
So we need to count the total possible pairs of ‘2 and 5’ in the expression to get the maximum value n such that the expression is divisible by10n
CALCULATION:
[34×65×82×105×126×2512×208×1016×1520]
It can be written in prime factorization form:
⇒[34×25×35×26×25×55×212×36×524×216×58
×216×516×320×520]
Now need to find total power of 2 and 5 in the expression:
Total power of 2 = 5 + 6 + 5 + 12 + 16 + 16 = 60
Total power of 5 = 5 + 24 + 8 + 16 + 20 = 73
Now,
The number of possible pairs of ‘2 and 5’ in the expression = 60 (minimum of two)
∴ Maximum value of ‘n’ will be 60 such that the expression is divisible by 10n