Greatest common divisor of fractions and decimals

In summary, the conversation discusses the possibility of calculating the greatest common divisor of decimals and fractions. It is noted that this is only defined for integers and cannot be calculated for fractions or irrational numbers. The need for a specific definition of divisor and multiple is also mentioned in order for this calculation to be possible.
  • #1
topito2
37
1
Is it possible to calculate the greatest common divisor of decimals and fractions? As far as I know, the greatest common divisor is a number you can calculate for integers, but I wonder if it's possible to calculate it for decimals and fractions.
 
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  • #2
No. "Least common multiple" and "greatest common divisor" are only defined for integers. If you allow fractions or irrational numbers, then any number, other than 0, can be a "common multiple" or "common divisor" so there are no "least" or "greatest".
 
  • #3
You will have to define divisor and multiple for this to work. One possibility: for positive rational numbers x,y, say x divides y if y/x is an integer. With this definition, gcd and lcm can be defined.
 

FAQ: Greatest common divisor of fractions and decimals

What is the definition of a greatest common divisor (GCD)?

A greatest common divisor is the largest number that divides evenly into two or more numbers.

How is the GCD of fractions and decimals calculated?

The GCD of fractions and decimals can be calculated by finding the greatest common divisor of the numerator and denominator of each fraction or decimal. This can be done by finding the prime factors of each number and then identifying the common factors.

Can the GCD of fractions and decimals be greater than 1?

Yes, the GCD of fractions and decimals can be greater than 1. This occurs when there are common factors present in both the numerator and denominator.

What is the relationship between the GCD and lowest common denominator (LCD)?

The GCD and LCD are closely related as the GCD is a factor of the LCD. The LCD is the smallest number that is divisible by both denominators in a fraction, and the GCD is a factor of this number.

Why is finding the GCD important?

Finding the GCD is important because it allows us to simplify fractions and decimals, making calculations easier. It is also used in various mathematical operations such as addition, subtraction, and multiplication of fractions and decimals.

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