Factor Calculator

How to use this factor calculator

What this calculator does

This calculator lists the positive integer factors of a whole number: the positive integers that divide it with no remainder. With a second number, it also identifies the positive factors shared by both inputs. It is useful for checking arithmetic, simplifying ratios and fractions, spotting divisibility patterns, and preparing for greatest-common-divisor work. The tool is intentionally about positive factors of positive integers; it does not factor algebraic expressions, decimals, or negative inputs, and it does not attempt industrial-scale integer factorization.

When to use it

Use it when you need to verify the complete divisor list for a homework problem, compare two integers before simplifying a fraction, confirm whether a proposed number divides evenly, or inspect shared factors before calculating a greatest common divisor. OpenStax's discussion of factors and divisibility tests provides a concise mathematical reference for the same underlying ideas.

How to calculate

1. The calculator opens with the demonstration values 84 and 126, so the results and example Excel workbook are immediately available. Replace Number #1 with any supported positive integer.
2. If you want a comparison, enter Number #2. Leave it blank when you only need one factor list. Results update automatically as soon as the current input is valid.
3. Read the factor-count pills and the detailed factor lists, then choose Download Excel to export the current validated model. Reset clears both numbers and the results; export remains unavailable until a valid Number #1 is entered again.

Input guide

Number #1 is required. Enter a positive integer from 1 through 1,000,000,000,000. Plain digits such as 360 and standard comma-grouped integers such as 1,000 are accepted. Decimals, scientific notation, signs, spaces inside digits, and ambiguous comma forms are rejected rather than silently reinterpreted. Increasing the number does not necessarily increase its factor count: a large prime can have only two positive factors, while a smaller composite number may have many. A common mistake is to enter a decimal or assume that every number below the input is a factor.

Number #2 is optional and follows the same integer format and range. Entering it activates the shared-factor comparison. For example, 126 alongside 84 produces eight common positive factors. A second number with no shared factor except 1 will still produce a valid common-factor list containing 1. Leaving Number #2 blank is not an error; it simply removes the comparison result.

Output guide

Number #1: ... factors and Number #2: ... factors report the counts of distinct positive divisors for each entered integer. Common: ... factors reports how many positive divisors occur in both sets when Number #2 is present. Factors of Number #1 and Factors of Number #2 show the complete ascending lists, including 1 and the number itself. Common factors is the intersection of those lists, also shown in ascending order. These are exact integer identities for the supported input range, not estimates or recommendations.

Worked example

The startup example uses 84 and 126. Factor pairs for 84 include 1×84, 2×42, 3×28, 4×21, 6×14, and 7×12, giving the 12 positive factors 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The 12 positive factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126. Their intersection is 1, 2, 3, 6, 7, 14, 21, 42, so the first-open display correctly reports 8 common factors. OpenStax also explains how divisor lists connect to prime, composite, and greatest-common-divisor concepts.