On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ?0123

Step 1: First, we need to find the original number. We know that when a number is divided by 68, the quotient is 269 and the remainder is 0. We can use the formula for division which is:

Dividend = Divisor * Quotient + Remainder

In this case, the Dividend is our original number, the Divisor is 68, the Quotient is 269, and the Remainder is 0. Substituting these values into the formula gives us:

Original number = 68 * 269 + 0 = 18292

Step 2: Now, we need to find the remainder when this original number (18292) is divided by 67. We can use the formula for division again, but this time we don't know the remainder. So, we can rearrange the formula to solve for the remainder:

Remainder = Dividend - (Divisor * Quotient)

We know the Dividend (18292) and the Divisor (67), but we don't know the Quotient. However, we can find the Quotient by dividing the Dividend by the Divisor:

Quotient = Dividend / Divisor = 18292 / 67 = 273 (rounded down to the nearest whole number because the quotient of a division is always a whole number)

Now we can substitute these values into the formula to find the remainder:

Remainder = 18292 - (67 * 273) = 31

So, the remainder when the original number is divided by 67 is 31.