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When 876 is added to another three-digit number 2P3, we get a four-digit number 10Q9, which is divisible by 11. The value of P-Q is _____.

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Important Questions on Number Systems

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There is a 22-digit number which consists of only one digit – from 1, 2, 3, 4, 5, or 6. For example, 11111111......11, 22222222......22, ......, 66666666......66. Such a number is always divisible by _____.
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The product of the factors of 72 is _____.
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The number of ways of expressing 72 as a product of two factors is _____.
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In how many ways can 144 be expressed as a product of two distinct factors?
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How many numbers lie between 100 and 1000 such that they leave a remainder of 3 when divided by 7, and leave a remainder of 4 when divided by 11?
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The highest common factor of two natural numbers a and b is 10, while their lowest common multiple of is 45. If a=15, then what is the value of b?
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The respective LCM and HCF of 10! and 15! are _____.