Last updated: July 31, 2026
Integer Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
sum = a + b, difference = a - b, product = a × b, quotient = trunc(a/b), remainder = a mod b, gcd(a,b), lcm = |a×b|/gcd when gcd ≠ 0.
Where:
- a=First integer
- b=Second integer
- gcd=Greatest common divisor
- lcm=Least common multiple
Worked Examples
Positive integer pair
Evaluate a = 12 and b = 8.
- 1Add to get 20.
- 2Subtract to get 4.
- 3Multiply to get 96.
- 4Compute quotient 1, remainder 4, gcd 4, and lcm 24.
Mixed signs
Evaluate a = -7 and b = 3.
- 1Add to get -4 and subtract to get -10.
- 2Product is -21.
- 3Truncated quotient is -2 and remainder is -1.
- 4gcd is 1, so lcm is |(-7)(3)|/1 = 21.
Zero in the first input
Evaluate a = 0 and b = 9.
- 1Add and subtract using 0.
- 2Product is 0.
- 3Quotient is 0 and remainder is 0.
- 4gcd is 9 and lcm is 0 because one factor is zero.
Division-by-zero warning case
Enter a = 5 and b = 0.
- 1The calculator still reports sum, difference, product, gcd, and lcm-related safe values.
- 2Quotient and remainder are marked with an error because division by zero is undefined.
- 3Use the warning message to correct the second input.
Introduction
Integers show up everywhere: counts, debts, scores, indices, divisibility, and modular arithmetic. This calculator goes beyond simple arithmetic by showing not only sum, difference, and product, but also division behavior, gcd, and lcm from the same two inputs.
What Counts as an Integer
Integers include negative whole numbers, zero, and positive whole numbers. They do not include fractional or decimal parts.
..., -3, -2, -1, 0, 1, 2, 3, ...
Integers are closed under addition, subtraction, and multiplication.
Division of integers does not always produce an integer.
Many number theory topics begin with integer inputs.
Core Arithmetic Outputs
The calculator reports sum, difference, and product immediately because these are the most common operations for a pair of integers.
Sum combines both values.
Difference measures how far a is above or below b.
Product captures repeated addition or scaling.
Signs matter in every arithmetic output.
Quotient and Remainder
For integer division, the quotient here is truncated toward zero to match JavaScript behavior, and the remainder comes from the % operator.
12 ÷ 8 gives quotient 1 remainder 4.
-7 ÷ 3 gives quotient -2 remainder -1.
Division by zero is undefined.
Quotient and remainder are often used together in modular reasoning.
Because truncation is used, negative-division results may differ from a floor-division convention taught in some math contexts.
Why GCD and LCM Matter
The greatest common divisor measures shared divisibility, while the least common multiple measures the first positive number both integers divide into evenly.
gcd(12, 8) = 4.
lcm(12, 8) = 24.
If one input is 0, lcm becomes 0 in this implementation.
Euclidean-style gcd logic is fast and reliable.
Use gcd to simplify fractions and lcm to combine repeating cycles or common denominators.
How Signs Affect Results
Sign rules drive nearly every output, especially product, quotient, and remainder.
Positive × positive = positive.
Negative × positive = negative.
gcd is reported as a non-negative value.
lcm is reported as non-negative when defined.
Division by Zero Handling
If b = 0, quotient and remainder are undefined. The calculator returns a safe payload with an explicit error message instead of throwing an exception.
Sum still equals a.
Difference still equals a.
Product is 0 because a × 0 = 0.
gcd defaults to |a| and lcm to 0 in the error payload.
How to Use the Tool
Enter two integers and then scan the outputs in layers: arithmetic first, then quotient and remainder, then divisibility metrics.
Enter a.
Enter b.
Check the primary sum output.
Use gcd and lcm for number-theory follow-up work.
FAQs
What operations does this integer calculator perform?
It returns sum, difference, product, truncated quotient, remainder, gcd, and lcm for two integer inputs.
Why are inputs rounded in the wrapper?
The wrapper converts numeric entries to the nearest integers so the calculator stays focused on integer operations.
What does truncated quotient mean?
It means the decimal part of a/b is discarded toward zero, so -7/3 becomes -2 instead of -3.
Can the remainder be negative?
Yes. In JavaScript, the % operator keeps the sign of the dividend, so -7 % 3 is -1.
Why is gcd always non-negative?
Greatest common divisor is typically reported as a non-negative magnitude, regardless of the signs of the inputs.
What happens when one input is zero?
The gcd becomes the absolute value of the other number, and the lcm becomes 0 in this implementation.
Why does division by zero return an error field?
Quotient and remainder are undefined when b = 0, so the calculator returns a descriptive error while still providing safe numeric fields.
Is this calculator useful for number theory homework?
Yes. It is especially helpful for checking divisibility, Euclidean-algorithm intuition, and lcm/gcd relationships.