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When is added to another three-digit number , we get a four-digit number , which is divisible by . The value of is _____.
(a)
(b)
(c)
(d)

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Important Questions on Number Systems
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There is a -digit number which consists of only one digit – from , , , , , or . For example, , , , . Such a number is always divisible by _____.

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The product of the factors of is _____.

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The number of ways of expressing as a product of two factors is _____.

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In how many ways can be expressed as a product of two distinct factors?

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How many numbers lie between and such that they leave a remainder of when divided by , and leave a remainder of when divided by ?

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The HCF of and is _____.

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The highest common factor of two natural numbers and is , while their lowest common multiple of is . If , then what is the value of ?

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The respective and of and are _____.
