# What is the largest value of n in 45 n which can exactly divide 6250!

| What is the largest value of n in 45

^{n}which can exactly divide 6250!A. 1562

B. 1561

C. 1560

D. None of these

### Right Answer is: C

#### SOLUTION

45 = 9 5 = 3^{2} 5

Now we calculate power of 3 and 5 individually in 6250!

We need two power of 3 to make one power of 45, so we will divide power of 3 (i.e. 3120) by 2

So 3^{3120} 5^{1562} = (3^{2})^{1560} 5^{1562}

Hence the largest value of n in 45^{n} is 1560 which can exactly divide 6250!

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What is the largest value of n in 45 n which can exactly divide 6250!