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awholenumber
- 200
- 10
When we try to find the Greatest common factor (GCF) of two numbers , does it only involve prime factorization ?
Yes.rosekidcute said:Ok , so the same prime factorization is used to find the LCM too , right ?
rosekidcute said:Thanks for the information mfb , i am just trying to cover the algebra 1 for dummies book .
It doesn't have a method like this LCM(a, b)=a*b/GCD(a, b) mentioned in it .
rosekidcute said:lol ok , first let me somehow finish this one book properly
FactChecker said:Yes. The GCF is a product of primes but is not usually a prime itself. Prime factorization of both numbers is the way to find out what the GCF is. If you have the prime factorization of both numbers, it is easy to calculate the GCF.
This is wrong. Euclid's very efficient algorithm for finding GCDs does not require doing anything at all with prime numbers.FactChecker said:Yes. The GCF is a product of primes but is not usually a prime itself. Prime factorization of both numbers is the way to find out what the GCF is. If you have the prime factorization of both numbers, it is easy to calculate the GCF.
Yes, that has been mentioned in post 6 for example.Michael Hardy said:But you don't need to know anything about prime factorizations to find the GCD; you can use Euclid's algorithm, which is very efficient.
The Greatest Common Factor (GCF) is the largest number that is a factor of two or more given numbers. In other words, it is the largest number that divides evenly into all of the given numbers without any remainders.
To find the GCF of two or more numbers, you can use the prime factorization method. First, write out the prime factorization of each number. Then, identify the common prime factors and multiply them together to find the GCF.
Finding the GCF is important because it helps simplify fractions and expressions, and it is also useful in finding the lowest common denominator in fractions. It is also used in various mathematical operations, such as simplifying algebraic expressions and solving equations.
Yes, the GCF can be greater than the smallest number in a given set of numbers. This is because the GCF is the largest number that is a factor of all the given numbers, so it is not limited by the smallest number in the set.
Yes, there is a difference between GCF and LCM. GCF is the largest number that is a factor of two or more numbers, while LCM is the smallest number that is a multiple of two or more numbers. However, they are related in that the product of the GCF and LCM of two numbers is equal to the product of the two numbers themselves.