Using divisibility test, to determine which of the following numbers is divisible by 2 , by 3 , by 4 , by 5 , by 6 , by 8 , by 9 , by 10 , by 11 (say, yes or no). Number Divisible by 2 3 4 5 6 8 9 10 11 128 Yes No Yes No No Yes No No No 990 1586 275 6686 639210 429714 2856 3060 406839

A number is divisible by 2 , if it has any of the digits 0 , 2 , 4 , 6 or 8 in its unit's place. If the sum of the digits of the number is divisible by 3 then the number is divisible by 3 . If a number is divisible by 4 , then the last two digits (that is one's and ten's place) of that number should be divisible by 4 . If the number is divisible by both 2 and 3 then the number is divisible by 6 . Above we have seen that all the numbers are divisible by 2 and 3 . So, they are all also divisible by 6 . If the number formed by the last three digits is divisible by 8 then the number is divisible by 8 . If the sum of the digits of the number is divisible by 9 then the number is divisible by 9 . If the last/unit digit of the number is 0 then the number is divisible by 10 . In the given numbers, the unit digit of all the numbers is 0 , thus they all are divisible by 10 . A number is said to be divisible by 11 if the difference between the sum of digits at odd places and even places of the number is 0 or divisible by 11 . Number Divisible by 2 3 4 5 6 8 9 10 11 128 Yes No Yes No No Yes No No No 990 Yes Yes No Yes Yes No Yes Yes Yes 1586 Yes No No No No No No No No 275 No No No Yes No No No No Yes 6686 Yes No No No No No No No No 639210 Yes Yes No Yes Yes No No Yes Yes 429714 Yes Yes No No Yes No Yes No No 2856 Yes Yes Yes No Yes Yes No No No 3060 Yes Yes Yes Yes Yes No Yes Yes No 406839 No Yes No No No No No No No Hence, this is the required answer

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Foundation Course Mathematics>Chapter 3 - Playing With Numbers>NCERT Section>Q 12

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A number which has more than two factors is called a .

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Important Questions on Playing With Numbers

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Foundation Course Mathematics>Chapter 3 - Playing With Numbers>NCERT Section>Q 12

The smallest prime number is _____.

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Foundation Course Mathematics>Chapter 3 - Playing With Numbers>NCERT Section>Q 12

The smallest composite number is _____.

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Foundation Course Mathematics>Chapter 3 - Playing With Numbers>NCERT Section>Q 12

The smallest even prime number is _____.

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Foundation Course Mathematics>Chapter 3 - Playing With Numbers>NCERT Section>Q 1

Using divisibility test, to determine which of the following numbers is divisible by $2$ , by $3$ , by $4$ , by $5$ , by $6$ , by $8$ , by $9$ , by $10$ , by $11$ (say, yes or no).