
The exponent of 2 in the prime factorization of 144 is
(A) 2
(B) 4
(C) 1
(D) 6
Answer
449.6k+ views
11 likes
Hint: First of all, break 144 as the multiplication of small integers. We know the property that when nothing is given then the exponent of that number is 1. We also know the formula for simplification when two numbers with the same base and different exponents, . Now, simplify it further and get the exponent of 2.
Complete step-by-step solution
According to the question, we are given a number and we have to find the exponent of 2 in its prime factorization.
Here, first of all, we need the prime factorization of 144.
We know that prime factorization is the breakdown of an integer into smaller integers. In other words, we can say that in the prime factorization method, an integer is written as the multiplication of small integers.
Also, we can say that the exponent refers to the number of times a number is multiplied by itself.
For prime factorization of 144, we need its factors.
From the above, we can observe that
144 = …………………………………………(1)
We know the property that when nothing is given then the exponent of that number is 1 ……………………………………(2)
We also know the formula for simplification when two numbers with the same base and different exponents, …………………………………………………………………(3)
Now, from equation (1), equation (2), and equation (3), we get
144 = ……………………………………………(4)
From the above equation, we have the number which is the exponent of 2.
Therefore, the exponent of 2 in the prime factorization of 144 is 4. Hence, the correct option is (B).
Note: Here, one point should be kept into consideration. The exponent is equal to 1 when nothing is given. For instance, if we have a number a. Since nothing is mentioned here, So the exponent of a is 1.
Complete step-by-step solution
According to the question, we are given a number and we have to find the exponent of 2 in its prime factorization.
Here, first of all, we need the prime factorization of 144.
We know that prime factorization is the breakdown of an integer into smaller integers. In other words, we can say that in the prime factorization method, an integer is written as the multiplication of small integers.
Also, we can say that the exponent refers to the number of times a number is multiplied by itself.
For prime factorization of 144, we need its factors.
From the above, we can observe that
144 =
We know the property that when nothing is given then the exponent of that number is 1 ……………………………………(2)
We also know the formula for simplification when two numbers with the same base and different exponents,
Now, from equation (1), equation (2), and equation (3), we get
144 =
From the above equation, we have the number which is the exponent of 2.
Therefore, the exponent of 2 in the prime factorization of 144 is 4. Hence, the correct option is (B).
Note: Here, one point should be kept into consideration. The exponent is equal to 1 when nothing is given. For instance, if we have a number a. Since nothing is mentioned here, So the exponent of a is 1.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE
