Answer
Verified
410.4k+ views
Hint: In this question, we find the greatest common factor of two numbers. We find the greatest common factor in the two methods. The first method is, we find the factor of given numbers. Then we choose the common numbers from the factorization of these numbers, the greatest common number is the greatest common factor of given two numbers. And the second method is, we find the prime factor of each number. Then choose the common numbers from prime factorization of given numbers. After that multiply, these numbers and the number which comes after multiplication is the greatest common factor.
Complete step by step solution:
In this question, the word greatest common factor is used. First, we know about the greatest common factor. The greatest common factor is defined as the largest positive integer which is divided by the given number without the reminder.
It is denoted as GCF.
Now we come to the question. To find the greatest common factor of two numbers, there are two methods.
First method:
First, we find the factor of given numbers \[20\] and \[30\] as below.
Now,
We find the factor of \[20\].
The factors of \[20\] are as below.
\[20 = 20,\;10,\;5,\;4,\;2,1.................\left( 1 \right)\]
Then,
We find the factor of \[30\].
The factors of \[30\] are as below.
\[30 = 30,\;15,\;10,\;6,\;5,\;3,\;2,\;1.................\left( 2 \right)\]
Now,
We find the common form equation \[\left( 1 \right)\;{\text{and}}\left( 2 \right)\].
Thus, the common numbers from the factors of \[20\] and \[30\] are as below.
\[ = 10,\;5,\;2,\;1\]
The greatest common number is \[10\].
Therefore, the greatest common factor of \[20\] and \[30\] is\[10\].
Second method:
We write the prime factorization of \[20\] and \[30\].
The prime factors of \[20\] are.
\[ \Rightarrow 20 = 2 \times 2 \times 5\]
The prime factors of \[30\] are.
\[ \Rightarrow 30 = 2 \times 3 \times 5\]
The common form factors are \[2\] and \[5\].
Then we multiply these two numbers.
\[ \Rightarrow 2 \times 5 = 10\]
Therefore, the greatest common factor of \[20\] and \[30\] is \[10\].
Note:
If you have two numbers and you want to find the greatest common factor of these two numbers. Then first you find the factor of the given two numbers. After that, you choose the common numbers from the factorization of given numbers. Thus, the greatest number from the common numbers of factorization is the greatest common factor.
Complete step by step solution:
In this question, the word greatest common factor is used. First, we know about the greatest common factor. The greatest common factor is defined as the largest positive integer which is divided by the given number without the reminder.
It is denoted as GCF.
Now we come to the question. To find the greatest common factor of two numbers, there are two methods.
First method:
First, we find the factor of given numbers \[20\] and \[30\] as below.
Now,
We find the factor of \[20\].
The factors of \[20\] are as below.
\[20 = 20,\;10,\;5,\;4,\;2,1.................\left( 1 \right)\]
Then,
We find the factor of \[30\].
The factors of \[30\] are as below.
\[30 = 30,\;15,\;10,\;6,\;5,\;3,\;2,\;1.................\left( 2 \right)\]
Now,
We find the common form equation \[\left( 1 \right)\;{\text{and}}\left( 2 \right)\].
Thus, the common numbers from the factors of \[20\] and \[30\] are as below.
\[ = 10,\;5,\;2,\;1\]
The greatest common number is \[10\].
Therefore, the greatest common factor of \[20\] and \[30\] is\[10\].
Second method:
We write the prime factorization of \[20\] and \[30\].
The prime factors of \[20\] are.
\[ \Rightarrow 20 = 2 \times 2 \times 5\]
The prime factors of \[30\] are.
\[ \Rightarrow 30 = 2 \times 3 \times 5\]
The common form factors are \[2\] and \[5\].
Then we multiply these two numbers.
\[ \Rightarrow 2 \times 5 = 10\]
Therefore, the greatest common factor of \[20\] and \[30\] is \[10\].
Note:
If you have two numbers and you want to find the greatest common factor of these two numbers. Then first you find the factor of the given two numbers. After that, you choose the common numbers from the factorization of given numbers. Thus, the greatest number from the common numbers of factorization is the greatest common factor.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE