What will be the HCF of 0.25 and 1.25?

Question

Prepp Team · Accepted Answer

Finding the HCF of Decimal Numbers 0.25 and 1.25

The Highest Common Factor (HCF) of two or more numbers is the largest number that divides all of them exactly. When dealing with decimal numbers, the easiest way to find their HCF is to convert them into integers.

Steps to Calculate HCF of Decimals

To find the HCF of 0.25 and 1.25, we can follow these steps:

Convert the given decimal numbers into whole numbers by multiplying them by a suitable power of 10. The power of 10 should be large enough to remove the decimal point from all the numbers. In this case, the maximum number of decimal places is two (in 0.25 and 1.25), so we multiply by $10^2 = 100$.
Calculate the HCF of the resulting whole numbers.
Divide the HCF of the whole numbers by the same power of 10 that was used in step 1.

Step-by-Step Calculation

Let's apply the steps to find the HCF of 0.25 and 1.25.

Step 1: Convert to whole numbers

$0.25 \times 100 = 25$
$1.25 \times 100 = 125$

Now we need to find the HCF of 25 and 125.

Step 2: Find the HCF of 25 and 125

We can find the HCF using methods like prime factorization or listing factors.

Using Prime Factorization:

Prime factors of $25 = 5 \times 5 = 5^2$
Prime factors of $125 = 5 \times 5 \times 5 = 5^3$

The common prime factor is 5. The lowest power of the common prime factor is $5^2$.

So, HCF(25, 125) = $5^2 = 25$.

Alternatively, by listing factors:

Factors of 25: 1, 5, 25
Factors of 125: 1, 5, 25, 125

The common factors are 1, 5, and 25. The largest common factor is 25.

So, HCF(25, 125) = 25.

Step 3: Divide the HCF by the power of 10

We found the HCF of 25 and 125 is 25. We multiplied the original numbers by 100.

HCF(0.25, 1.25) = $\frac{\text{HCF}(25, 125)}{100} = \frac{25}{100} = 0.25$

Therefore, the HCF of 0.25 and 1.25 is 0.25.

Summary Table

Decimal Numbers	Multiplied by 100	Resulting Integers	HCF of Integers	HCF of Decimals (HCF of Integers / 100)
0.25	$\times 100$	25	25	0.25
1.25	$\times 100$	125	25	0.25

Revision Table: Understanding HCF Concepts

Concept	Explanation	Example
HCF (Highest Common Factor)	The largest number that divides two or more numbers without leaving a remainder. Also known as the Greatest Common Divisor (GCD).	HCF(12, 18) = 6
Finding HCF of Integers	Methods include prime factorization or listing all factors and finding the largest common one.	For HCF(25, 125): Factors of 25 are 1, 5, 25. Factors of 125 are 1, 5, 25, 125. Common factors are 1, 5, 25. HCF is 25.
Finding HCF of Decimals	Convert decimals to integers by multiplying by a power of 10, find the HCF of integers, then divide the result by the same power of 10.	HCF(0.2, 0.4): Convert to 2, 4. HCF(2, 4) = 2. Divide by 10: 2/10 = 0.2. So HCF(0.2, 0.4) = 0.2.

Additional Information on HCF Calculation

Finding the HCF of numbers, whether integers or decimals, is a fundamental concept in number theory with various applications, including simplifying fractions and solving problems involving division.

For numbers with differing numbers of decimal places, multiply by the power of 10 corresponding to the highest number of decimal places among the numbers. For instance, for 0.5, 1.20, and 3.75, you would multiply by 100 because 3.75 has two decimal places, which is the maximum.
The HCF of two numbers is always less than or equal to the smallest of the two numbers. In our case, HCF(0.25, 1.25) = 0.25, which is equal to the smaller number.
If two numbers are co-prime (have no common factors other than 1), their HCF is 1. For example, HCF(7, 11) = 1.