Finding the Highest Common Factor (HCF) of Decimals

To find the Highest Common Factor (HCF) of decimal numbers like 4.08 and 6.63, it's often easiest to convert them into whole numbers first. We can do this by multiplying both numbers by a power of 10 that makes them integers. In this case, both numbers have two decimal places, so multiplying by 100 will work.

• Convert 4.08 to a whole number: $4.08 \times 100 = 408$
• Convert 6.63 to a whole number: $6.63 \times 100 = 663$

Now, the problem is reduced to finding the HCF of the whole numbers 408 and 663.

Calculating HCF of 408 and 663

We can find the HCF using the prime factorization method.

• Find the prime factorization of 408:
  • $408 = 2 \times 204$
  • $204 = 2 \times 102$
  • $102 = 2 \times 51$
  • $51 = 3 \times 17$
  • So, $408 = 2^3 \times 3 \times 17$
• Find the prime factorization of 663:
  • $663 = 3 \times 221$ (Since the sum of digits $6+6+3=15$ is divisible by 3)
  • To factor 221, we can test prime numbers. It's not divisible by 2, 3, 5, 7, 11.
  • Let's try 13: $221 \div 13 = 17$
  • So, $663 = 3 \times 13 \times 17$

Now, let's identify the common prime factors and their lowest powers:

The common prime factors are 3 and 17. The lowest power of 3 is $3^1$ and the lowest power of 17 is $17^1$.

HCF of 408 and 663 is the product of these common factors raised to their lowest powers:

HCF$(408, 663) = 3 \times 17 = 51$

Converting HCF back to Decimal

Since we initially multiplied the original decimal numbers by 100 to get the whole numbers 408 and 663, we must now divide the HCF we found (which is 51) by 100 to get the HCF of the original decimal numbers.

HCF$(4.08, 6.63) = \text{HCF}(408, 663) \div 100 = 51 \div 100 = 0.51$

Final Answer on HCF of 4.08 and 6.63

The Highest Common Factor of 4.08 and 6.63 is 0.51.

Revision Table: HCF Calculation Steps

Additional Information: Understanding HCF

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two or more numbers is the largest positive integer that divides each of the numbers without leaving a remainder. When dealing with decimal numbers, the method involves converting them to whole numbers, finding the HCF of the whole numbers, and then scaling the result back to the decimal format based on the initial conversion factor.

Understanding HCF is crucial in various mathematical operations, including simplifying fractions and solving problems involving distribution or grouping into equal parts.