What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?
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Question 14 Real Numbers Exercise 1B

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What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

Answer:

Prime factors of 4, 7 and 13

4 = 2x2

7 and 13 are prime numbers.

LCM ( 4, 7, 13) = 364

We know that, the largest 4 digit number is 9999

Step 1: Divide 9999 by 364, we get

9999/364 = 171

Step 2: Subtract 171 from 9999

9999 - 171 = 9828

Step 3: Add 3 to 9828

9828 + 3 = 9831

Therefore 9831 is the number.

What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?
What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

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100 Questions 80 Marks 90 Mins

Given:

The greatest number divisible by 6, 7, 8, and 12.

Concept used:

LCM method used

Calculation:

Now finding the LCM,

6 = 3 × 2

7 = 7 × 1

8 = 2 × 2 × 2

12 = 2 × 2 × 3

So, required LCM = 2× 2 × 2 × 3 × 7 = 168

Therefore, the number has to be of form 168 x + 4, where x is an integer.

The largest number of 5 digits is 99999

When divided by 168, 99999 leaves the remainder 39, which is

99999 = 168 × 595 + 39

So, 99999 - 39 = 99960 which is divisible by 168.

Now as it leaves a remainder 4 in each case

Therefore, the required number is 99960 + 4 = 99964

∴ The correct answer is 99964.

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What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

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What is the greatest 5 digit number which when divided by 2 3 4 5 and 6 leaves a remainder of 1 in each case and when divided by 7 leaves no remainder?

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