Question

On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder

is 11. If the number lies between 500 and 600, then the remainder on dividing the number by 19 is​

Answer 1

On dividing a natural number by 13, the remainder is 3 and on dividing the same number by 21, the remainder is 11.

The number lies between 500 and 600.

We have to find, remainder on dividing the number by 19.

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☯ Let the number be x.

According to givEn condition,

The number lies between 500 and 600.

Therefore,

➯ 500 < x < 600

★ On dividing x by 21 the remainder will be 11.

For the number between 500 and 600 there will be only 5 such number which leave remainder 11 on dividing with 21.

such as, 515, 536, 557, 578, 599.

☯ Let's check the second condition,

★ Dividing all number with 13 -

• 515 = 39 × 13 + 8

• 536 = 41 × 13 + 3

• 557 = 42 × 13 + 11

• 578 = 44 × 13 + 6

• 599 = 46 × 13 + 1

As we can see that,

536 is the number with leave remainder 3 on dividing with 13.

∴ 536 is the natural number.

Now, We can find the remainder on dividing the number by 19.

➯ 536 ÷ 19 = 28 × 19 + 4 = 532 + 4

∴ Remainder is 4 on dividing the number 536 by 19.

Answer 2

Answer:

We have,

⬤ Divisor - Quotient

→ 13 - 3 = 21 - 11 = 10

Now,

LCM (13,21) = 13 × 21 = 273

Now, 273 is least common multiple of 13 and 21

Thus, The multiple of 273 will also be common multiple of 13 and 21.

Therefore, Between 500 and 600 multiple of 273 is :

↪ 273 × 2

↪546

Now, Required dividend = 546 (Common difference between division and quotient)

᠉ 546 - 10

᠉ 536

So, Remainder on Dividing 336 by 19 we get :

➥ 336/19

➥ 4