Find the remainder when 22225555+ 55552222 is divided by 7a)2b)4c)0d)3...
Given number: 22225555 55552222
Divisor: 7
To find the remainder when the given number is divided by 7, we will use the concept of divisibility by 7.
Divisibility Rule for 7:
A number is divisible by 7 if the difference between twice the last digit and the remaining leading truncated number is divisible by 7.
Step 1: Splitting the given number
We can split the given number into two parts: 22225555 and 55552222.
Step 2: Finding the remainder for each part
a) 22225555:
The last digit is 5, and the leading truncated number is 2222555.
Twice the last digit is 2 * 5 = 10.
The difference between twice the last digit and the leading truncated number is 10 - 2222555 = -2222545.
b) 55552222:
The last digit is 2, and the leading truncated number is 5555222.
Twice the last digit is 2 * 2 = 4.
The difference between twice the last digit and the leading truncated number is 4 - 5555222 = -5555218.
Step 3: Summing up the remainders
To find the remainder when the given number is divided by 7, we need to sum up the remainders obtained in step 2.
-2222545 + (-5555218) = -7777763
Step 4: Simplifying the result
To simplify the result, we will divide -7777763 by 7.
-7777763 ÷ 7 = -1111119
Step 5: Finding the positive remainder
Since the remainder must always be positive, we take the absolute value of -1111119.
|-1111119| = 1111119
Step 6: Finalizing the answer
The remainder when 22225555 55552222 is divided by 7 is 1111119.
Hence, the correct answer is option 'C' (0).