Defining Prime Factors, Greatest Common Factor, Least Common Multiple

In summary, prime factors are factors of a number which are prime, and the least common multiple is the smallest number that is a multiple of two or more given numbers.
  • #1
kupid
34
0
I am a commerce student
But i decided to refresh my maths from some basics , i downloaded this book called algebra one for dummies .

I have few doubts .

What is the difference between

Prime factors
Greatest common factor (GCF)
Least common multiple (LCM)

Can i move to algebra factorization after learning these ?
 
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  • #2
Re: I decided to refresh my maths from basics and i have few doubts ?

stallman said:
I am a commerce student
But i decided to refresh my maths from some basics , i downloaded this book called algebra one for dummies .

I have few doubts .

What is the difference between

Prime factors
Greatest common factor (GCF)
Least common multiple (LCM)

Can i move to algebra factorization after learning these ?

They are totally different

let me explain prime factors

before that let me explain prime number

A prime number is a number which does not have any factor other than 1 and itself

for example 7 is a prime as no number other than 1 and 7 divide it
but 6 is not a prime as 2 and 3 divide it
bt definition 1 is not a prime

prime factor is a factor of the number which is prime

for example for 42 the factors are 1,2,3,6,7,14,21,42 out of which 2,3,7 are prime factors and 6,14,21 and 42 are composite (not prime) factors

I hope explanation is clear
 
  • #3
Re: I decided to refresh my maths from basics and i have few doubts ?

Thanks a lot for explaining prime numbers and prime factors , these little things have always been confusing

Could you also explain

Greatest common factor (GCF)
and
Least common multiple (LCM)

?
 
  • #4
Re: I decided to refresh my maths from basics and i have few doubts ?

kupid said:
Thanks a lot for explaining prime numbers and prime factors , these little things have always been confusing

Could you also explain

Greatest common factor (GCF)
and
Least common multiple (LCM)

?

The greatest common factor is the largest number that will divide two or more numbers. For example, we have:

\(\displaystyle \text{gcf}(8,12)=4\)

4 is the largest number that divides both 8 and 12, and we can determine this by computing the prime factorization of both numbers:

\(\displaystyle 8=2^3\)

\(\displaystyle 12=2^2\cdot3\)

So, we look for the prime factors which are common to both, which is this case is 2, and we take the lower power found which is:

\(\displaystyle 2^2=4\)

The least common multiple is the smallest number that is a multiple of two or more given numbers.

For example, we have:

\(\displaystyle \text{lcm}(8,12)=24\)

This can be found by taking all prime factors found in at least one of the numbers, with it's highest power. We see we have 2 as a factor and it's highest power is 3, and we see we have a 3 present, and it's highest power is 1, and so we obtain:

\(\displaystyle \text{lcm}(8,12)=2^3\cdot3=24\)
 
  • #5
Re: I decided to refresh my maths from basics and i have few doubts ?

Thanks Mark , i think i need to work with some examples before i can move on to the next lessons :)
 

FAQ: Defining Prime Factors, Greatest Common Factor, Least Common Multiple

What are prime factors?

Prime factors are the numbers that can divide into a given number without any remainder. They are the building blocks of a number and are always prime numbers (numbers that are only divisible by 1 and themselves).

What is the greatest common factor (GCF)?

The greatest common factor (GCF) is the largest number that can evenly divide into two or more given numbers. It is also known as the greatest common divisor (GCD).

What is the least common multiple (LCM)?

The least common multiple (LCM) is the smallest number that is a multiple of two or more given numbers. It is also known as the lowest common multiple (LCM) or the smallest common multiple.

How do you find the prime factors of a number?

To find the prime factors of a number, you can use a method called factorization. This involves dividing the number by its smallest prime factor until the result is a prime number. You can continue this process until all the prime factors have been found.

How do you find the GCF and LCM of two or more numbers?

To find the GCF and LCM of two or more numbers, you can use a method called prime factorization. First, find the prime factors of each number. Then, the GCF is the product of all the common prime factors and the LCM is the product of all the prime factors, including the common ones.

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