Factor Calculator – Find All Factors, Factor Pairs & Factor Tree

The factor calculator finds every factor of any integer instantly. Enter a number, click calculate, and get all factors, factor pairs, and a visual factor tree in seconds.

No formulas needed. No long division by hand. The tool handles numbers up to 999,999,999.

Factors come up in simplifying fractions, finding the GCF, splitting groups evenly, and solving word problems. Getting them right matters.

What Is a Factor of a Number?

A factor is any integer that divides evenly into another number. No remainder left over.

For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly.

1 and the number itself are always factors. Every integer has at least two factors. The only exception is 1, which has exactly one factor: itself.

Factor vs. multiple: A factor divides into a number. A multiple is the number multiplied by something. 6 is a factor of 24. 24 is a multiple of 6.

Factor vs. divisor: Same thing. Both words describe a number that divides evenly into another.

How to Find Factors of a Number

You only need to check integers up to the square root of n. Every factor below the square root has a matching factor above it.

Steps:

1. Start at 1 and divide n by each integer
2. If the remainder is 0, both the divisor and quotient are factors
3. Stop when the divisor exceeds √n
4. List all factors in ascending order

Example: factors of 36

• √36 = 6, so check 1 through 6
• 36 ÷ 1 = 36 ✓
• 36 ÷ 2 = 18 ✓
• 36 ÷ 3 = 12 ✓
• 36 ÷ 4 = 9 ✓
• 36 ÷ 5 = 7.2 ✗
• 36 ÷ 6 = 6 ✓

All factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Total: 9 factors.

Factor Pairs Explained

A factor pair is two numbers that multiply together to give the original number. Every factor has exactly one partner.

For 24: 1 × 24, 2 × 12, 3 × 8, 4 × 6. Four factor pairs.

How to count factor pairs from total factors:

• Even number of factors: total ÷ 2 pairs
• Odd number of factors: (total − 1) ÷ 2 pairs, plus the square root pairs with itself
• Numbers with an odd factor count are always perfect squares

Factor pairs of common numbers:

Number	Factor Pairs
12	(1,12) (2,6) (3,4)
24	(1,24) (2,12) (3,8) (4,6)
36	(1,36) (2,18) (3,12) (4,9) (6,6)
48	(1,48) (2,24) (3,16) (4,12) (6,8)
60	(1,60) (2,30) (3,20) (4,15) (5,12) (6,10)
72	(1,72) (2,36) (3,24) (4,18) (6,12) (8,9)

Factor Calculator – Three Tools in One

This factor calculator runs three modes. Each one solves a different part of factoring.

Tab 1 – All Factors

Shows every factor of any number up to 999,999,999. Results appear as color-coded chips.

• Purple chips: prime numbers
• Blue chips: composite numbers
• Factor pairs table below the chips
• Copy all factors button for easy transfer

Tab 2 – Factor Tree

Draws a visual tree breaking the number into its prime building blocks. Works for numbers up to 9,999.

• Blue circles mark prime numbers (no further splitting)
• Grey circles mark composite numbers (keep splitting)
• The bottom row reads as the prime factorization

Tab 3 – Divisibility

Checks 11 divisibility rules at once (2 through 12). Green cards mean divisible. Red cards mean not divisible.

Each card shows the rule so you understand why, not just whether.

All Factors of Common Numbers

These are the complete factor lists.

Number	All Factors	Total
12	1, 2, 3, 4, 6, 12	6
16	1, 2, 4, 8, 16	5
18	1, 2, 3, 6, 9, 18	6
20	1, 2, 4, 5, 10, 20	6
24	1, 2, 3, 4, 6, 8, 12, 24	8
28	1, 2, 4, 7, 14, 28	6
30	1, 2, 3, 5, 6, 10, 15, 30	8
32	1, 2, 4, 8, 16, 32	6
36	1, 2, 3, 4, 6, 9, 12, 18, 36	9
40	1, 2, 4, 5, 8, 10, 20, 40	8
42	1, 2, 3, 6, 7, 14, 21, 42	8
45	1, 3, 5, 9, 15, 45	6
48	1, 2, 3, 4, 6, 8, 12, 16, 24, 48	10
50	1, 2, 5, 10, 25, 50	6
54	1, 2, 3, 6, 9, 18, 27, 54	8
56	1, 2, 4, 7, 8, 14, 28, 56	8
60	1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60	12
63	1, 3, 7, 9, 21, 63	6
64	1, 2, 4, 8, 16, 32, 64	7
72	1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72	12
75	1, 3, 5, 15, 25, 75	6
80	1, 2, 4, 5, 8, 10, 16, 20, 40, 80	10
84	1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84	12
90	1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90	12
96	1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96	12
98	1, 2, 7, 14, 49, 98	6
100	1, 2, 4, 5, 10, 20, 25, 50, 100	9
108	1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108	12
120	1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120	16
144	1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144	15
180	1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180	18
360	1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360	24

What Is a Prime Number and Why It Matters for Factoring

A prime number has exactly two factors: 1 and itself. No more, no less.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

Composite numbers have more than two factors. 12 is composite because it has six factors.

1 is neither prime nor composite. It stands alone.

Why this matters: Every composite number breaks down into a unique set of prime factors. This is called the fundamental theorem of arithmetic. The factor tree shows exactly how.

Factor Tree Method: Step-by-Step

A factor tree splits a number into two factors repeatedly. Stop when every branch ends in a prime.

Factor tree of 60:

        60
       /  \
      6    10
     / \   / \
    2   3  2   5

Bottom row: 2 × 3 × 2 × 5 = 60. Written as: 2² × 3 × 5.

Factor tree of 84:

        84
       /  \
      4    21
     / \   / \
    2   2  3   7

Bottom row: 2 × 2 × 3 × 7 = 84. Written as: 2² × 3 × 7.

Factor tree of 120:

         120
        /   \
       8     15
      / \   /  \
     2   4  3    5
        / \
       2   2

Result: 2³ × 3 × 5 = 120.

The calculator draws this tree automatically for any number up to 9,999.

Greatest Common Factor (GCF) Using Factor Lists

The greatest common factor is the largest factor shared by two numbers.

Method: list factors of both numbers, find the largest match.

GCF of 12 and 18:

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Common factors: 1, 2, 3, 6
• GCF = 6

GCF of 24 and 36:

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• GCF = 12

GCF of 48 and 72:

• GCF = 24

When the GCF of two numbers equals 1, those numbers are called coprime. They share no common factors beyond 1.

GCF is different from LCM. GCF is the largest shared factor. LCM is the smallest shared multiple. According to Khan Academy, GCF and LCM work together in fraction simplification.

The factor calculator handles all factors, pairs, and the factor tree in one place. For the greatest common factor of two numbers, use the GCF Calculator. For the least common multiple, the LCM Calculator covers that separately.

Divisibility Rules for Quick Factoring

Divisibility rules let you spot factors without dividing. Useful for large numbers.

Divisor	Rule
2	Last digit is 0, 2, 4, 6, or 8
3	Sum of all digits is divisible by 3
4	Last two digits form a number divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
7	Double the last digit, subtract from the rest, repeat
8	Last three digits divisible by 8
9	Sum of all digits is divisible by 9
10	Last digit is 0
11	Alternating digit sum (left to right) is divisible by 11
12	Divisible by both 3 and 4

Example: Is 360 divisible by 9?

3 + 6 + 0 = 9. Yes, 9 divides 9 exactly. So 360 is divisible by 9.

The Divisibility tab in the factor calculator runs all 11 checks simultaneously.

Factors of Negative Numbers

Negative integers have both positive and negative factor pairs.

Factors of -12:

• (+1, -12), (-1, +12)
• (+2, -6), (-2, +6)
• (+3, -4), (-3, +4)

The tool shows positive factors by default. For most classroom and GCF work, positive factors are all you need.

Negative factors become relevant in algebra when factoring expressions like x² – 5x + 6.

How Many Factors Does a Number Have?

Use prime factorization to count factors without listing them all.

Formula: If n = p¹ᵃ × p²ᵇ × p³ᶜ, total factors = (a+1)(b+1)(c+1)

Examples:

• 12 = 2² × 3¹ → (2+1)(1+1) = 6 factors
• 36 = 2² × 3² → (2+1)(2+1) = 9 factors
• 48 = 2⁴ × 3¹ → (4+1)(1+1) = 10 factors
• 100 = 2² × 5² → (2+1)(2+1) = 9 factors
• 360 = 2³ × 3² × 5¹ → (3+1)(2+1)(1+1) = 24 factors

Numbers with an odd factor count are always perfect squares. 36, 100, and 144 all have odd factor counts.

Factors in Real-World Use

Factors are not just for math class. They show up in everyday problems.

• Simplifying fractions: Divide numerator and denominator by their GCF
• Splitting groups evenly: Find factors to split 60 students into equal rows
• Tiling problems: Factor pairs of 48 tell you possible rectangle dimensions
• Scheduling: Factors of 24 help with shift rotations and time blocks
• Cryptography: Large number factorization underpins RSA encryption. No efficient algorithm exists for very large primes, which is why RSA works, as confirmed by MIT OpenCourseWare.

Frequently Asked Questions

Conclusion

The factor calculator finds all factors, factor pairs, and draws a factor tree for any integer you enter. The divisibility tab checks 11 rules at once so you can spot factors without dividing.

For classroom work, GCF problems, fraction simplification, or just checking your math, this tool handles it in one click.