Factors of 27 Calculator – Find All Divisors & Prime Factorisation

Factors Finder

Enter a positive integer

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.

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 (but factor pairs are 1×27 and 3×9).
Fraction simplification: 9/27 = 1/3, 18/27 = 2/3, etc.
Number theory: 27 is the smallest cube greater than 1 that is also the sum of two squares? Not exactly, but it's used in modular arithmetic.

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. In number theory, 27 is also the fourth hyperfactorial? Not exactly, but it appears in the “27 Club” and in many puzzles.

Factor Pairs of 27

1 × 27
3 × 9

Common Mistakes When Finding Factors of 27

Forgetting 9: Since 3×9, 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 not prime).

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 factors of 27?

Test divisibility from 1 up to the square root of 27 (~5.2). 1 divides 27, 3 divides 27, then include the paired factors: 9 and 27.

What is the prime factorisation of 27?

27 = 3 × 3 × 3 = 3³. This is because 27 is a perfect cube (3³).

How many factors does 27 have?

27 has 4 factors. Using the prime factorisation 3³, number of factors = (3+1) = 4.