The HCF of ${3^5}$, ${3^9}$ and ${3^{14}}$ is:
(A) ${3^5}$
(B) ${3^9}$
(C) ${3^{14}}$
(D) ${3^{21}}$
Last updated date: 31st Mar 2023
•
Total views: 207.9k
•
Views today: 4.85k
Answer
207.9k+ views
Hint: There are various methods for finding the highest common factor of the given numbers. The simplest method is to find the highest common factor is by prime factorization method. In the prime factorization method, we first represent the given two numbers as a product of their prime factors and then find the product of the lowest powers of all the common factors.
Complete step by step solution:
In the given question, we are required to find the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$.
To find the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$, first we find out the prime factors of all the numbers.
Prime factors of ${3^5}$$ = 3 \times 3 \times 3 \times 3 \times 3$
Prime factors of ${3^9}$$ = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
Prime factors of ${3^{14}}$$ = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
Now, the highest common factor is the product of the lowest powers of all the common factors.
Now, we can see that there is only one repeated factor,$3$ in all the numbers.
Hence, least common multiple of ${3^5}$, ${3^9}$ and ${3^{14}}$$ = 3 \times 3 \times 3 \times 3 \times 3$
$ = {3^5}$
Hence, the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$ is ${3^5}$.
Note:
Highest common factor is the greatest number that divides both the given numbers. Similarly, the highest common factor can also be found by using the prime factorization method as well as using Euclid’s division lemma. Highest common divisor is just a product of common factors with lowest power. Highest common factor can also be calculated by division method as well as by using Euclid’s division lemma.
Complete step by step solution:
In the given question, we are required to find the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$.
To find the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$, first we find out the prime factors of all the numbers.
Prime factors of ${3^5}$$ = 3 \times 3 \times 3 \times 3 \times 3$
Prime factors of ${3^9}$$ = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
Prime factors of ${3^{14}}$$ = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
Now, the highest common factor is the product of the lowest powers of all the common factors.
Now, we can see that there is only one repeated factor,$3$ in all the numbers.
Hence, least common multiple of ${3^5}$, ${3^9}$ and ${3^{14}}$$ = 3 \times 3 \times 3 \times 3 \times 3$
$ = {3^5}$
Hence, the highest common factor of ${3^5}$, ${3^9}$ and ${3^{14}}$ is ${3^5}$.
Note:
Highest common factor is the greatest number that divides both the given numbers. Similarly, the highest common factor can also be found by using the prime factorization method as well as using Euclid’s division lemma. Highest common divisor is just a product of common factors with lowest power. Highest common factor can also be calculated by division method as well as by using Euclid’s division lemma.
Recently Updated Pages
Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
