MHB Defining Prime Factors, Greatest Common Factor, Least Common Multiple

[kupid]

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 ?

 

[kaliprasad]

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

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

 

[kupid]

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)

?

 

[MarkFL]

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)

?

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

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

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

$$8=2^3$$

$$12=2^2\cdot3$$

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:

$$2^2=4$$

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

For example, we have:

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

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:

$$\text{lcm}(8,12)=2^3\cdot3=24$$

 

[kupid]

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 :)