Class 10 Exam > Class 10 Questions > Find the sum of the exponents of the prime fa...
Start Learning for Free
Find the sum of the exponents of the prime factors in the prime factorization of 196.
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the sum of the exponents of the prime factors in the prime factor...
We have 196 = 22 × 72
2 + 2 = 4
2 + 2 = 4
Free Test
FREE
| Start Free Test |
Community Answer
Find the sum of the exponents of the prime factors in the prime factor...
To find the sum of the exponents of the prime factors in the prime factorization of 196, we first need to find the prime factorization of 196.
Prime factorization is the process of breaking down a number into its prime factors, which are the prime numbers that divide the original number without leaving a remainder.
Prime factorization of 196:
- We can start by dividing 196 by the smallest prime number, which is 2. 196 divided by 2 equals 98.
- Next, we continue dividing by 2 until we can no longer divide evenly. 98 divided by 2 equals 49.
- Now, we divide 49 by the next prime number, which is 7. 49 divided by 7 equals 7.
- Since 7 is a prime number, we stop here.
The prime factorization of 196 is 2^2 * 7^2.
To find the sum of the exponents, we add the exponents of each prime factor:
- The exponent of 2 is 2.
- The exponent of 7 is also 2.
Adding these exponents together, we get 2 + 2 = 4.
Therefore, the sum of the exponents of the prime factors in the prime factorization of 196 is 4.
Hence, the correct answer is option C, 4.
Prime factorization is the process of breaking down a number into its prime factors, which are the prime numbers that divide the original number without leaving a remainder.
Prime factorization of 196:
- We can start by dividing 196 by the smallest prime number, which is 2. 196 divided by 2 equals 98.
- Next, we continue dividing by 2 until we can no longer divide evenly. 98 divided by 2 equals 49.
- Now, we divide 49 by the next prime number, which is 7. 49 divided by 7 equals 7.
- Since 7 is a prime number, we stop here.
The prime factorization of 196 is 2^2 * 7^2.
To find the sum of the exponents, we add the exponents of each prime factor:
- The exponent of 2 is 2.
- The exponent of 7 is also 2.
Adding these exponents together, we get 2 + 2 = 4.
Therefore, the sum of the exponents of the prime factors in the prime factorization of 196 is 4.
Hence, the correct answer is option C, 4.
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Question Description
Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?.
Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?.
Solutions for Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the sum of the exponents of the prime factors in the prime factorization of 196.a)2b)3c)4d)5Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup