Factors of 27 Calculator – Find All Divisors & Prime Factorisation

Factors Finder

Enter a positive integer

Factors of 27: 1, 3, 9, 27

Factor pairs: 1 × 27, 3 × 9

Prime factorisation: 3^3

Total factors: 4

Step‑by‑Step

Number: 27

Step 1: Find all pairs of integers whose product is 27.

1 × 27

3 × 9

Step 2: Collect all unique numbers from these pairs.

Factors: 1, 3, 9, 27

Step 3: Count the factors – total = 4

Step 4: Prime factorisation – divide 27 by the smallest prime repeatedly.

27 = 3^3

Tip: 27 is a perfect cube (3³). Its factors come in pairs: 1×27, 3×9.

The Factors of 27 Calculator finds all positive divisors of 27 (or any number you enter), lists factor pairs, shows prime factorisation, and counts the total number of factors. 27 is a perfect cube (3³) and its factors are 1, 3, 9, and 27. Understanding the factors of 27 helps in simplifying fractions, finding greatest common divisors, solving geometry problems (e.g., volume of a cube), and many real‑world situations involving groups of 27.

Factors of 27 – Full List

1, 3, 9, 27

4 factors in total

How to Find the Factors of 27

Step 1: Since √27 ≈ 5.2, test numbers from 1 to 5.

Step 2: 1 divides 27 → factors 1 and 27.

Step 3: 2 does not divide 27.

Step 4: 3 divides 27 → factors 3 and 9.

Step 5: 4 does not divide 27.

Step 6: 5 does not divide 27.

Result: All factors: 1, 3, 9, 27.

Prime Factorisation of 27

27 ÷ 3 = 9, 9 ÷ 3 = 3, 3 ÷ 3 = 1. So 27 = 3 × 3 × 3 = 3³. Using the exponent formula, the number of factors = (3+1) = 4, which matches our list.

Key Definitions for Factors of 27

Perfect Cube (27): An integer produced by multiplying a whole number by itself three times ($3^3 = 3 \times 3 \times 3 = 27$).
Divisors of 27: The four unique positive integers (1, 3, 9, 27) that divide 27 without leaving a remainder.
Factor Pairs of 27: The sets of two integers that multiply together to yield 27: $(1 \times 27)$ and $(3 \times 9)$.

Powers of 3 & Factors Complete Reference Table

Number (n)	All Divisor Factors	Factor Pairs	Prime Factorisation	Total Factors	Classification
9	1, 3, 9	1×9, 3×3	3²	3	Perfect Square (3²)
18	1, 2, 3, 6, 9, 18	1×18, 2×9, 3×6	2 × 3²	6	Abundant Composite
27	1, 3, 9, 27	1×27, 3×9	3³	4	Perfect Cube (3³)
36	1, 2, 3, 4, 6, 9, 12, 18, 36	1×36, 2×18, 3×12, 4×9, 6×6	2² × 3²	9	Perfect Square & Cube Multiple
54	1, 2, 3, 6, 9, 18, 27, 54	1×54, 2×27, 3×18, 6×9	2 × 3³	8	Multiple of 27
81	1, 3, 9, 27, 81	1×81, 3×27, 9×9	3⁴	5	4th Power of 3 (3⁴)

Real‑World Applications of Factors of 27

Geometry: A cube with volume 27 cubic units has side length 3 (cube root). Surface area = 6 × 3² = 54.
Grouping: 27 items can be arranged in 4 different rectangular layouts: 1×27, 3×9, 9×3, 27×1 (factor pairs 1×27 and 3×9).
Fraction simplification: 9/27 = 1/3, 18/27 = 2/3, etc.

Why 27 Is a Perfect Cube

27 = 3 × 3 × 3 = 3³, making it a perfect cube. Its cube root is 3. In geometry, a cube of side 3 has volume 27 cubic units.

Factor Pairs of 27

1 × 27
3 × 9

Common Mistakes When Finding Factors of 27

Forgetting 9: Since 3×9 = 27, both 3 and 9 must be included.
Including 0 or negative numbers: Factors are positive for basic arithmetic.
Not recognising 27 as a perfect cube: Its prime factorisation is 3³, not 3×9 (where 9 is composite).

Use this factors of 27 calculator to check your homework, explore other numbers, or teach factorisation concepts. The step‑by‑step output shows the systematic trial‑division method.

Step‑by‑Step Manual Example (27)

Input: 27
√27 ≈ 5.2, test i = 1 to 5:
i=1 → 27÷1=27 → add 1, 27
i=2 → not divisible
i=3 → 27÷3=9 → add 3, 9
i=4 → not divisible
i=5 → not divisible
Sorted: 1, 3, 9, 27

Frequently Asked Questions about Factors of 27

What are the factors of 27?

The factors of 27 are 1, 3, 9, and 27. These numbers divide 27 exactly without leaving a remainder.

How do you find all factors of 27?

Test divisibility from 1 up to √27 (≈ 5.2). 1 divides 27 (pair 1×27) and 3 divides 27 (pair 3×9). 2, 4, and 5 do not divide 27.

What is the prime factorisation of 27?

The prime factorisation of 27 is 3 × 3 × 3 = 3³. 27 is a perfect cube.

How many factors does 27 have?

27 has exactly 4 factors. Using the prime exponent formula for 3³, total factors = (3 + 1) = 4.

What are the factor pairs of 27?

The factor pairs of 27 are (1, 27) and (3, 9) because 1 × 27 = 27 and 3 × 9 = 27.

Is 27 a prime or composite number?

27 is a composite number because it has more than two factors (1, 3, 9, 27).

Is 27 a perfect square or perfect cube?

27 is a perfect cube (3³ = 27) with cube root 3. It is not a perfect square.

How is the factor of 27 used in geometry?

A 3D cube with volume 27 cubic units has side length 3 units, face area 9 square units, and total surface area 54 square units.