HCF of Decimal Numbers

Last Updated : 23 Jul, 2025

Highest Common Factor of two or more numbers is the largest positive number that divides each of the numbers without leaving a remainder.

Example: HCF of 1.2 and 1.8 is 0.6

HCF (Highest Common Factor) of decimal numbers is the largest decimal number that can divide both decimals exactly To find the HCF of Decimal Numbers we simply need to convert them into whole numbers.

Finding the HCF of decimal numbers follows a simple step-by-step process i.e.,

  1. Multiply the decimal numbers by a power of 10 to convert the decimals to whole numbers.
  2. Find the HCF of these whole numbers.
  3. Adjust by the appropriate power of 10 based on the number of decimal places by dividing the HCF you obtained by the same power of 10 that you used in step 1.

Examples on HCF of Decimal Numbers

Let's consider some more solved examples for better understanding.

Example 1: Finding HCF of 3, 2.7, and 0.09
Solution:

Convert to Whole Numbers:
3.00, 2.70, 0.09 (2 decimal places for all)

Calculate the Multiplier: n = 102 = 100

After removing Decimal Points: 300, 270, 9,
Now, we need to find HCF(300, 270, 9)

Prime Factorization:

300 = 22 × 31 × 52
270 = 21 × 33 × 51
9 = 32

Calculate HCF:
HCF = 2min⁡(2, 1, 0) × 3min⁡(1, 3, 2) × 5min⁡(2, 1, 0) = 20 × 31 × 50 = 3

Adjust Result: HCF = 3/100 = 0.03

Example 2: Finding HCF of 0.216, 6, and 2
Solution:

Given Numbers: 0.216, 6, and 2

Calculate the Multiplier:
n = 103 = 1000

Convert to Whole Numbers:

0.216 × 1000 = 216
6.000 × 1000 = 6000
2.000 × 1000 = 2000

Now, we have to find the HCF(216, 6000, 2000)

Prime Factorization:

216 = 23 x 33
6000 = 24 × 31 × 53
2000 = 24 × 53

Calculate HCF:
HCF = 2min⁡(3, 4, 4) × 3min⁡(3, 1, 0) × 5min⁡(0, 3, 3) = 23 × 30 × 50 = 8

Adjust Result: HCF = 8/1000 = 0.008

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