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Find the highest power of 11 that will divide into 1000! exactly.
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You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by 3, 5 and by 7...
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6! = 6 × 5 × 4 × 3 × 2 × 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4) = 45. What is the highest power of two that divides exactly into 100!?
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Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
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Can you reconstruct the long division calculation from the 'skeleton'?
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Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
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How many zeros are there at the end of the number which is the product of first hundred positive integers?
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Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?
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