Find the best tutors and institutes for Class 10 Tuition
Q1(iii):
Express each number as a product of its prime factors: (iii) 3825
Solution :
Given: The number $3825$.
To Find: The prime factorization of $3825$.
Step 1: Testing for divisibility by the smallest prime numbers.
We begin by testing the divisibility of $3825$ using the rules of divisibility for prime numbers in ascending order ($2, 3, 5, 7, 11, \dots$).
Check for $2$: The last digit of $3825$ is $5$, which is odd. Therefore, $3825$ is not divisible by $2$.
Check for $3$: The sum of the digits of $3825$ is $3 + 8 + 2 + 5 = 18$. Since $18$ is divisible by $3$, the number $3825$ is divisible by $3$.
$3825 \div 3 = 1275$
Step 2: Continuing the factorization of the quotient.
Now, we factorize $1275$.
Check for $3$: The sum of the digits of $1275$ is $1 + 2 + 7 + 5 = 15$. Since $15$ is divisible by $3$, $1275$ is divisible by $3$.
$1275 \div 3 = 425$
Step 3: Continuing the factorization of the new quotient.
Now, we factorize $425$.
Check for $3$: The sum of the digits of $425$ is $4 + 2 + 5 = 11$. Since $11$ is not divisible by $3$, $425$ is not divisible by $3$.
Check for $5$: The last digit of $425$ is $5$. According to the divisibility rule for $5$, any number ending in $0$ or $5$ is divisible by $5$.
$425 \div 5 = 85$
Step 4: Continuing the factorization of the new quotient.
Now, we factorize $85$.
Check for $5$: The last digit of $85$ is $5$.
$85 \div 5 = 17$
Step 5: Identifying the final prime factor.
The number $17$ is a prime number, meaning its only factors are $1$ and itself.
$17 \div 17 = 1$
Step 6: Expressing the number as a product of prime factors.
Combining all the prime factors obtained from the divisions above:
$3825 = 3 \times 3 \times 5 \times 5 \times 17$
Using exponential notation to group identical factors:
$3825 = 3^2 \times 5^2 \times 17^1$
Final Answer: The prime factorization of $3825$ is $3^2 \times 5^2 \times 17$.
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(ii): Express each number as a product of its prime factors: (ii) 156
- 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
Top Tutor
Sector 43, Gurgaon
12 yrs of
Exp
1000
per hour
Online Classes
Student's Home
Experienced Mathematics and Science Educator | 10+ Years in Teaching and Coaching I have over a decade of experience in teaching and coaching students in Mathematics and Science. I have worked as a PGT Mathematics teacher at GBL Convent School, and have also taught Classes 9 and 10 (Maths & Science) at R.S. Education Hub. My teaching approach focuses on building strong conceptual clarity, personalized attention, and result-oriented strategies to help students excel academically. I have successfully guided numerous students through school exams, board exams, and foundational competitive preparation.
Top Tutor
Sonari, Jamshedpur
1 yrs of
Exp
4 students
657 hrs of classes completed
300
per hour
Online Classes
Student's Home
Tutor's home
I have a Science background completed my electrical engineering.... I am giving home tuition for 2 years.... I am also preparing for UPSC civil service exam.
Top Tutor
Sector 83, Gurgaon
20 yrs of
Exp
4 students
4201 hrs of classes completed
650
per hour
Online Classes
Tutor's home
For me, teaching is part of learning. As I am teaching I am also learning from my learners as they are diverse. Each learner in the classroom brings his or her unique background and ability. These are the elements that I invest in my teaching. Moreover, I allow learners to be themselves. This is a way of creating a conducive environment for learning.
Her method of teaching is very clear and student friendly. It’s really very easy for me to understand and also she has a lot of patience.
Super Tutor
Electronic City Phase I, Bangalore
20 yrs of
Exp
22 students
845 hrs of classes completed
400
per hour
Online Classes
Class 10 is a pivotal, fast-paced school year filled with a mix of academic preparation, growing responsibilities, and memorable moments with friends.Daily Routine and StudiesBusy schedules: Days involve attending subject-specific classes, taking detailed notes, and preparing for board exams.Favorite subjects: Time is often spent engaging deeply with core subjects like mathematics, science, and social studies.Extra help: Teachers provide extra guidance and revision sessions to help students handle exam stress.Friendships and Social LifeStronger bonds: Friendships deepen through shared lunch breaks, group studies, and mutual support during exams.Lasting memories: Small moments in the hallway or sharing stories in the classroom create a sense of a second family.
She teaches very well. I understand the concept very fast. She teaches smoothly always ask for any doubt. Very polite and calm in nature.
Shankar Vihar, Delhi
18 yrs of
Exp
Student's Home
We are teaching 8th, 9th,10th,11th,12th for the last 12 years and providing 95%+ in our subjects. We are giving best results in DELHI CANTT and South Delhi region.
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
