What is the quotient and remainder for 113 divided by 2
The correct answer and explanation is:
Let’s find the quotient and remainder when dividing 113 by 2.
Calculation:
- Divide 113 by 2.
- 2 goes into 113 56 times because 2×56=1122 \times 56 = 112.
- The difference between 113 and 112 is 1, so the remainder is 1.
Answer:
- Quotient = 56
- Remainder = 1
Explanation (300 words):
When you divide one number by another, the result consists of two parts: the quotient and the remainder. The quotient tells you how many times the divisor fits completely into the dividend, and the remainder is what is left over after dividing.
In this case, the problem is to divide 113 by 2. The number 113 is the dividend, and 2 is the divisor.
- Finding the quotient:
We want to find how many whole times 2 fits into 113. We start by checking multiples of 2:- 2×50=1002 \times 50 = 100
- 2×55=1102 \times 55 = 110
- 2×56=1122 \times 56 = 112
- 2×57=1142 \times 57 = 114 (too big, since 114 > 113)
- Finding the remainder:
The remainder is what is left after subtracting the largest multiple of the divisor from the dividend: 113−112=1113 – 112 = 1 So, the remainder is 1. - Summary:
The division can be expressed as: 113=(2×56)+1113 = (2 \times 56) + 1 This means 113 divided by 2 equals 56 with a remainder of 1.
Practical significance:
Understanding quotient and remainder is important for many real-world applications, such as:
- Computer programming: Dividing numbers often requires handling remainders, especially in algorithms like hashing or distributing resources evenly.
- Everyday life: If you have 113 items and want to pack them in boxes of 2, you will have 56 full boxes and 1 item leftover.
- Mathematics: Division with remainder is the foundation for concepts like modular arithmetic, which is important in cryptography and number theory.
So, the quotient is 56 and the remainder is 1 when dividing 113 by 2.