Find the best tutors and institutes for Class 10 Tuition
Q1(ii):
Express each number as a product of its prime factors: (ii) 156
Solution :
Given: A composite number $156$.
To Find: The prime factorization of $156$, expressed as a product of its prime factors.
Step 1: Understanding Prime Factorization
Prime factorization is the process of expressing a composite number as a product of prime numbers. We will use the method of successive division by the smallest prime numbers ($2, 3, 5, 7, 11, \dots$) until the quotient becomes $1$.
Step 2: Sequential Division
We start by dividing $156$ by the smallest prime number, which is $2$:
$156 \div 2 = 78$
[Since $156$ is an even number, it is divisible by $2$ according to the divisibility rule for $2$.]
Next, we divide the quotient $78$ by $2$:
$78 \div 2 = 39$
[Since $78$ is an even number, it is divisible by $2$.]
Next, we check for divisibility of $39$ by the next prime number, $3$:
$39 \div 3 = 13$
[Since the sum of the digits of $39$ is $3 + 9 = 12$, which is divisible by $3$, $39$ is divisible by $3$ according to the divisibility rule for $3$.]
Finally, we check for divisibility of $13$ by the next prime number, $5, 7, 11, \dots$:
$13 \div 13 = 1$
[Since $13$ is a prime number, it is only divisible by $1$ and itself.]
Step 3: Compiling the Factors
Based on the divisions performed above, we can write $156$ as:
$156 = 2 \times 2 \times 3 \times 13$
Step 4: Expressing in Exponential Form
We group the repeated prime factors using exponents:
$156 = 2^2 \times 3^1 \times 13^1$
Final Answer: The prime factorization of $156$ is $2^2 \times 3 \times 13$.
More Questions from Class 10 Mathematics Real numbers EXERCISE 1.1
- Q1(i): Express each number as a product of its prime factors: (i) 140
- Q1(iii): Express each number as a product of its prime factors: (iii) 3825
- Q1(iv): Express each number as a product of its prime factors: (iv) 5005
- Q1(v): Express each number as a product of its prime factors: (v) 7429
- Q2(i): Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (i) 26 and 91
- Q2(ii): Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (ii) 510 and 92
- Q2(iii): Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$ HCF = product of the two numbers. (iii) 336 and 54
- Q3(i): Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21
- Q3(ii): Find the LCM and HCF of the following integers by applying the prime factorisation method. (ii) 17, 23 and 29
- Q3(iii): Find the LCM and HCF of the following integers by applying the prime factorisation method. (iii) 8, 9 and 25
- Q4: Given that HCF (306, 657) = 9, find LCM (306, 657).
- Q5: Check whether $6^n$ can end with the digit 0 for any natural number $n$.
- Q6: Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.
- Q7: There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
CBSE Solutions for Class 10 Mathematics Real numbers
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Real numbers
Super Tutor
Sector 5, Dwarka, Delhi
10 yrs of
Exp
13 students
1271 hrs of classes completed
600
per hour
Online Classes
I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and same education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). This works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and same education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. -------------------------------------------------------------------------------Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have a one-to-one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. I will start the classes immediately once the first kid enrolls. -------------------------------------------------------------------------------I took classes and batches in different institutions.
The experience with virendra sir was amazing. He did away with all my doubts and difficulties at all times , he is more than a teacher and a mentor to me. I'll always remember sir's debate's , scolding and care for me. Ty sir for making me a greater individual.
Top Tutor
Sikandra, Agra
4 yrs of
Exp
1 student
350
per hour
Online Classes
Student's Home
I can teach every topic very easily and make it stronger for the students.
Sir teaches very well, all topics are very well explained.He gives time for me to understand the topics
Top Tutor
Mahmoorganj Tulsipur, Varanasi
4 yrs of
Exp
12 students
700 hrs of classes completed
100
per hour
Online Classes
Teaching methodology is such that even weakest students can understand the concept very easily through real life analogy
Great teacher i understand subjects with better clarity now and he teaches great and it sure helped me alot
Top Tutor
Munirka, Delhi
3 yrs of
Exp
1 student
48 hrs of classes completed
200
per hour
Online Classes
I am a teacher since last 3-4 years. I have teaching tuition to students of class 9th and 10th CBSE board. In these covid times i prefer online classes and my subjects of expertise are science, maths ans social science.
Top Tutor
Vesu, Surat
20 yrs of
Exp
18 students
1260 hrs of classes completed
500
per hour
Online Classes
I have experience teaching Mathematics to Grade 10 students with a focus on strengthening fundamental concepts and preparing them for board examinations. I teach important topics such as Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Trigonometry, Coordinate Geometry, Statistics, and Probability. My teaching approach involves explaining concepts clearly, solving problems step by step, and giving regular practice from NCERT and previous years’ board exam papers. I also conduct tests, revision classes, and doubt-clearing sessions to track students’ progress. My goal is to make mathematics simple and interesting while helping students build confidence and achieve good results in their Grade 10 board exams.
Very good teacher. Patient with the students and understands where they are confused quickly. Motivates the students to be better too.
Find more Tutor for Real numbers in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
