Can You Find the HCF of 1.2 and 0.12?

Introduction

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is typically defined for integers. However, we can extend the concept to decimal numbers by converting them to integers. In this explanation, we will determine the HCF of the numbers 1.2 and 0.12 using two different methods—by scaling to integers and by converting to fractions.

Method 1: Converting to Integers by Scaling

1. Scale the Numbers:
   Multiply both numbers by 100 to eliminate the decimals.
2. Find the HCF of the Integers:
   Now, find the HCF of 120 and 12.
   • Since divides exactly (), the HCF of 120 and 12 is .
3. Scale Back to the Original Units:
   Since we multiplied by 100 initially, divide the HCF by 100 to return to the original scale.

Thus, the HCF of 1.2 and 0.12 is 0.12.

Method 2: Converting to Fractions

1. Convert the Decimals to Fractions:
   • can be written as , which simplifies to .
   • can be written as , which simplifies to .
2. Express with a Common Denominator:
   The denominators are 5 and 25. The least common denominator (LCD) is 25.
   • Convert to a fraction with denominator 25:

     \frac{6}{5} = \frac{6 \times 5}{5 \times 5} = \frac{30}{25}

3. Find the HCF of the Numerators:
   The HCF of the numerators 30 and 3 is 3.
4. Determine the HCF of the Fractions:
   Since both fractions have the same denominator (25), the HCF of the fractions is:

   \frac{\text{HCF of numerators}}{\text{Common denominator}} = \frac{3}{25}

   \frac{3}{25} = 0.12

Thus, the HCF of 1.2 and 0.12 is 0.12.

Conclusion

Both methods clearly demonstrate that the Highest Common Factor (HCF) of 1.2 and 0.12 is 0.12. By either scaling the decimals to integers or converting them to fractions and then finding the HCF of the numerators, we arrive at the same result.

Disclaimer: This explanation is for educational purposes and illustrates the process of finding the HCF for numbers expressed in decimal form by converting them to equivalent integers or fractions.

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