Question

which is the smallest 6 digit number when divided by 5,6,7,8 respectively gives remainder as 3,4,5,6

Answer 1

Which is the smallest 6 digit number when divided by 5,6,7,8 respectively gives remainder as 3,4,5,6.

Solution:

Division with remainder is finding the largest integer that is the product of a divider provides value not greater than the dividend. The required number is called incomplete quotient. The difference between the dividend and the product of a divider on a partial quotient is called the remainder, is always less than the divisor. The general form of a linear equation can be expressed as

$$a = b \times q + r$$

. In this equation, q can be referred to as the quotient and d as the divisor, while r as the remainder. The equation can be transformed to find the remainder as:

$$r = a - b \times q$$

. Additionally, a and b must be natural numbers, with b being non-zero. The quotient is the integer result (rounded down) of the division of a by b. The remainder must also be an integer. If a and b are natural numbers, with d non-zero, it can be proven that there exist unique integers q and r, such that

$$a = b \times q + r$$

and

$$0 \leq r < b$$

. The number q is called the quotient, while r is called the remainder.

Smallest number of 6 digits is 100000. If we check in our case the remainder is obtained for each value, respectively. To get smallest 6 digit number we can find multiply the numbers and subtract two. So, we get number 151198. We can check remainder:

1. $\frac{151198}{5} = 30239.6$ subtract 30239 and get 0.6 multiply the above by 5 that give the remainder of 3.

2. $\frac{151198}{6} = 25199.66667$ subtract 25199 and get 0.666666666 multiply the above by 6 that give the remainder of 4

3. $\frac{151198}{7} = 25199.71429$ subtract 25199 and get 0.714285714 multiply the above by 7 that give the remainder of 5.

4. $\frac{151198}{8} = 18899.75$ subtract 18899 and get 0.75 multiply the above by 8 that give the remainder of 6.

The 6 digit number when divided by 5,6,7,8 respectively gives remainder as 3,4,5,6 are 151198.