How to Find Factors of 102 Step by Step with Examples
The concept of factors of 102 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding how to find the factors of a number is a key skill that supports prime factorization, divisibility checks, and finding common multiples, which are all common exam topics for students.
Understanding Factors of 102
A factor of 102 refers to any whole number that can divide 102 exactly without leaving a remainder. This concept is widely used in factorization, divisibility rules, and finding the Highest Common Factor (HCF). Students and teachers use factors regularly in arithmetic, number theory, and even geometry-related topics.
List of Factors of 102
The factors of 102 are all positive integers that divide 102 with no remainder.
Factors of 102 Table
| Divisor | Paired Factor | Is Prime? |
|---|---|---|
| 1 | 102 | No |
| 2 | 51 | Yes (2) |
| 3 | 34 | Yes (3) |
| 6 | 17 | Yes (17) |
| 17 | 6 | Yes (17) |
| 34 | 3 | No |
| 51 | 2 | No |
| 102 | 1 | No |
This table shows all the positive factors of 102 and their pairs. The pairs make it easier to remember which numbers combine to give 102 when multiplied together.
How to Find Factors of 102 – Step-by-Step Method
To find the factors of 102, follow these steps:
1. Start with 1:
2. Next, check 2:
3. Then, try 3:
4. Check 4:
5. Test 5:
6. Try 6:
7. Continue testing each number up to 102:
8. The complete list: 1, 2, 3, 6, 17, 34, 51, 102.
Pair Factors of 102
Pair factors are two numbers that multiply to give 102. The pair factors of 102 are:
(1, 102)
(2, 51)
(3, 34)
(6, 17)
Negative pair factors can also be listed, such as (-1, -102) and (-2, -51), since the product is still positive 102.
Prime Factorization of 102
The prime factorization of 102 means breaking it into a product of its prime factors. Here is the step-by-step process:
1. Start with the smallest prime, 2:
2. Next, try 3 (since 51 is divisible by 3):
3. Finally, 17 is itself a prime number.
4. So, the prime factors of 102 are 2, 3, and 17.
5. Prime factorization in product form: 102 = 2 × 3 × 17.
Worked Example – Solving a Factor Problem
1. Find all factors of 102 using division:
Keep only those that leave a remainder of 0.
Final answer: 1, 2, 3, 6, 17, 34, 51, 102.
2. What number multiplied by 17 gives 102?
n = 102 ÷ 17 = 6
Practice Problems
- List all the factors of 102.
- Is 8 a factor of 102?
- What are the prime factors of 102?
- Find all positive and negative pair factors of 102.
- Is 51 a factor of 102? How do you know?
Common Mistakes to Avoid
- Confusing multiples with factors (e.g., thinking 204 is a factor, but it’s a multiple).
- Forgetting negative pairs: every positive pair has a negative counterpart.
- Missing prime factorization or stopping before the number is fully broken into primes.
- Including decimal results as factors (only whole numbers are factors).
Real-World Applications
Understanding factors of 102 can help in areas such as grouping items, splitting amounts equally, and solving puzzles and LCM/HCF problems that appear in many competitive exams. Vedantu helps students build a strong grasp of such concepts with live and interactive classes.
Related Pages and Further Learning
- Factors of 105 – Compare other three-digit numbers.
- Prime Numbers – Learn more about prime factors.
- Factors of 12 – Try factorization of a smaller number.
- Tables 2 to 20 – Multiplication basics for finding factors quickly.
- Factors of 51 – 51 is itself a factor of 102, so compare their factors.
- Multiples of 4 – Understand the difference between factors and multiples.
- HCF of Two Numbers – See how common factors are used to find HCF.
- Factors of 36 – Explore factor pairs for another composite number.
- Factors of a Number – General methods and practice for any number.
- Difference Between Square and Rectangle – Application of factors in area problems.
- Tables 2 to 30 – For additional support on multiplication and divisibility.
- Factors of 103 – Compare consecutive numbers and factorization patterns.
We explored the idea of factors of 102, how to calculate them, learnt about pair factors, and saw the stepwise approach to prime factorization. Practicing these methods with Vedantu can help you master factors, prepare for exams, and understand their real-world value.
FAQs on Factors of 102 – Complete List, Pairs, and Prime Factorization
1. What are the factors of 102?
The factors of 102 are the numbers that divide 102 exactly without leaving any remainder. These are 1, 2, 3, 6, 17, 34, 51, and 102. Knowing these factors helps in understanding divisibility and prime factorization.
2. How to find factors of 102 by division method?
To find the factors of 102 by division method, divide 102 by all numbers starting from 1 up to 102 and note those that give a quotient with zero remainder. The division steps are:
1. 102 ÷ 1 = 102
2. 102 ÷ 2 = 51
3. 102 ÷ 3 = 34
4. 102 ÷ 6 = 17
5. 102 ÷ 17 = 6
6. 102 ÷ 34 = 3
7. 102 ÷ 51 = 2
8. 102 ÷ 102 = 1.
These give all the factors of 102.
3. What are the prime factors of 102?
The prime factorization of 102 breaks it into prime numbers that multiply together to give 102. By dividing 102 by prime numbers stepwise:
1. 102 ÷ 2 = 51
2. 51 ÷ 3 = 17
3. 17 ÷ 17 = 1.
Therefore, the prime factors are 2, 3, and 17.
4. What are the factors of 102 in pairs?
The pair factors of 102 are pairs of numbers that multiply to give 102. The pairs are:
(1, 102), (2, 51), (3, 34), and (6, 17).
Similarly, their negative pairs (-1, -102), (-2, -51), (-3, -34), and (-6, -17) also multiply to 102.
5. Is 102 a factor of 204?
Yes, 102 is a factor of 204 because 204 divided by 102 equals 2 with no remainder. Hence, 102 × 2 = 204.
6. What is the HCF of 102?
The Highest Common Factor (HCF) of 102 with another number is the greatest number that divides both numbers exactly. For example, the HCF of 100 and 102 is 2, as it is the largest number dividing both without remainder.
7. What are the multiples of 102?
The multiples of 102 are numbers obtained by multiplying 102 by whole numbers, such as 102, 204, 306, 408, and so on. For example, the fifth multiple of 102 is 510 (102 × 5).
8. Why isn’t 5 a factor of 102?
5 is not a factor of 102 because 102 does not end with 0 or 5, which is a divisibility rule for 5. Dividing 102 by 5 leaves a remainder, so 5 cannot divide 102 exactly.
9. Why do students confuse factors and multiples for 102?
Students often confuse factors and multiples of 102 because both involve divisibility but in opposite directions: factors divide the number exactly, while multiples are products of the number with whole numbers. Clarifying this with examples and definitions helps avoid confusion.
10. Are negative numbers considered as factors?
Yes, negative numbers can be considered as factors since multiplying two negative numbers results in a positive product. Thus, the negative pairs of factors exist for 102, like (-1, -102), but in most school contexts, factors usually refer to positive integers only.
11. How do you check if a number is a prime factor of 102?
To check if a number is a prime factor of 102, see if it divides 102 exactly without remainder and if it is a prime number (only divisible by 1 and itself). For example, 17 divides 102 leaving no remainder and is prime, so it is a prime factor.
12. When is factorization important for algebra or LCM/HCF questions?
Factorization is crucial in algebra for simplifying expressions and solving equations. It also helps find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of numbers, which are essential in problem-solving and number theory applications.
