The least number which must be subtracted from 7278745 so as to obtain a sum that is divisible by 11 is:

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To find the least number to subtract from 7278745 to make it divisible by 11, we use the divisibility rule of 11.

Step 1: Calculate the difference between the sum of digits in odd positions and the sum of digits in even positions.

Number: 7 2 7 8 7 4 5
Positions (from right):
5 (1st, odd), 4 (2nd, even), 7 (3rd, odd), 8 (4th, even), 7 (5th, odd), 2 (6th, even), 7 (7th, odd)

Sum of digits at odd positions = 5 + 7 + 7 + 7 = 26
Sum of digits at even positions = 4 + 8 + 2 = 14

Difference = 26 - 14 = 12

Step 2: Find remainder when difference is divided by 11.
12 mod 11 = 1

Step 3: Since the difference modulo 11 is 1, the number leaves a remainder 1 when divided by 11.

Step 4: To make the number divisible by 11, subtract this remainder 1 from the number.

However, the question asks for the least number to subtract so that the result is divisible by 11. But we must verify the remainder of the entire number modulo 11.

Alternatively, calculate 7278745 mod 11:

Calculate remainder stepwise:

Divide 7278745 by 11:

11 * 661704 = 7278744

Remainder = 7278745 - 7278744 = 1

So remainder is 1.

Therefore, subtracting 1 will make it divisible by 11.

But the options given are 3, 1, 5, 2.

Answer is 1.

Double-checking the options, the correct answer is 1.

Hence, the least number to subtract is 1.

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