Without actual division, find the remainder when 379843 is divided by 3.
Remainder Calculation Using Divisibility Rule for 3
To find the remainder when a number is divided by 3 without performing the actual long division, we can use the divisibility rule of 3. This rule states that the remainder of a number when divided by 3 is the same as the remainder of the sum of its digits when divided by 3.
Applying the Divisibility Rule
The number given is 379843.
First, we need to find the sum of the digits of this number:
Sum = 3 + 7 + 9 + 8 + 4 + 3
Let's calculate the sum:
Sum = 10 + 9 + 8 + 4 + 3
Sum = 19 + 8 + 4 + 3
Sum = 27 + 4 + 3
Sum = 31 + 3
Sum = 34
Finding the Remainder of the Sum
Now, we need to find the remainder when this sum (34) is divided by 3.
We perform the division: $$ 34 \div 3 $$
We know that $3 \times 11 = 33$.
So, the remainder is:
Remainder = $34 - 33$
Remainder = 1
Conclusion
According to the divisibility rule of 3, the remainder when 379843 is divided by 3 is the same as the remainder when the sum of its digits (34) is divided by 3, which is 1.
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Important Questions from Divisibility and Remainder
If all positive divisors of 132 are arranged in descending order, then what digit will be at unit place of first divisor ?
If 3 2019 is divided by 10, then what is the remainder?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum.
Which of the following is/are correct?
1. S is always divisible by 74.
2. S is always divisible by 9.
select the correct answer using the code given below:
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
