Online Euclidean Division: Free Calculator

Our Euclidean division calculator allows you to quickly perform Euclidean division and obtain the quotient and remainder. The tool also displays the complete mathematical decomposition in school format.

What is Euclidean Division?

Euclidean division is a mathematical operation that consists of dividing one integer (the dividend) by another non-zero integer (the divisor). The result is composed of two parts:

• The quotient: the number of times the divisor is contained in the dividend
• The remainder: what remains after removing the largest multiple of the divisor

The Euclidean Division Formula

Euclidean division always follows this fundamental formula:

The remainder must always be positive and strictly less than the divisor.

How to Perform Euclidean Division?

Manual Method (School Method)

Let's take an example: divide 125 by 7.

1. Find how many times 7 can fit into 125
2. 7 × 17 = 119 (the largest multiple of 7 less than 125)
3. Calculate the remainder: 125 - 119 = 6
4. Result: quotient = 17 and remainder = 6
5. Verification: 7 × 17 + 6 = 119 + 6 = 125 ✓

Examples of Euclidean Divisions

Why Use Our Calculator?

• ✓ Fast and accurate: instant result without risk of error
• ✓ School format: presentation as in school
• ✓ Complete decomposition: mathematical formula displayed
• ✓ Free and unlimited: no registration required
• ✓ Educational: detailed explanations to understand