What Are the Factors and Prime Factorization of 38?
The concept of factors of 38 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding factors of a number like 38 helps students master divisibility, prime factorization, and arithmetic skills, which are crucial for quick calculations and competitive maths exams. Let's explore everything you need to know about the factors of 38.
Understanding Factors of 38
A factor of 38 is any whole number that divides 38 exactly without leaving any remainder. In other words, if you multiply two numbers and get 38, both numbers are factors of 38. This concept is widely used in prime factorization, division method, and listing factor pairs. Understanding the factors of 38 also builds the foundation for learning about multiples, common factors, HCF, and LCM.
How to Find Factors of 38?
To find the factors of 38, you look for all whole numbers that divide 38 perfectly, leaving zero remainder. Start with 1 and check up to 38:
Let’s use step-by-step division:
2. 38 ÷ 2 = 19 (so, 2 and 19 are factors)
3. 38 ÷ 19 = 2 (already listed above)
4. 38 ÷ 38 = 1 (already listed above)
Any other number between 1 and 38 does not divide 38 evenly. Therefore, the factors of 38 are 1, 2, 19, and 38.
List of Factors of 38
Here is the complete list of all positive and negative factors of 38:
Negative factors: -1, -2, -19, -38
Each negative factor simply makes the original number positive when divided.
Factor Pairs of 38
Factor pairs are two numbers that, when multiplied, give 38. The factor pairs of 38 are:
| Pair | Multiplication | Result |
|---|---|---|
| 1 and 38 | 1 × 38 | 38 |
| 2 and 19 | 2 × 19 | 38 |
| -1 and -38 | -1 × -38 | 38 |
| -2 and -19 | -2 × -19 | 38 |
These pairs show all the ways to multiply whole numbers to get 38.
Prime Factorization of 38
Prime factorization means expressing 38 as a product of prime numbers only. Let's do it step by step:
38 ÷ 2 = 19
2. 19 is a prime number, so it cannot be divided further except by 1 and itself.
3. Therefore, the prime factorization of 38 is 2 × 19.
A prime number is a number greater than 1 that has only two factors: 1 and itself.
Is 38 a Prime or Composite Number?
38 is a composite number because it has more than two distinct factors (1, 2, 19, 38). It can be divided evenly by numbers other than 1 and 38.
Multiples and Common Factors
Multiples of 38 are numbers you get by multiplying 38 by whole numbers (e.g., 38, 76, 114, 152, ...).
If you're asked about common factors (like factors of 38 and 39), list the factors for both numbers and find the numbers they share. For example:
- Factors of 39: 1, 3, 13, 39
- Common factors of 38 and 39: 1 only.
To dive deeper, visit Common Factors on Vedantu.
Worked Examples – Solving Problems on Factors of 38
Let’s solve a few questions step by step:
Step 1: List the factors: 1, 2, 19, 38
Step 2: Add them: 1 + 2 + 19 + 38 = 60
Step 3: Average = Total sum ÷ Number of factors = 60 ÷ 4 = 15
Question 2: Is 38 divisible by 4?
Step 1: Divide 38 by 4: 38 ÷ 4 = 9.5
Step 2: Since the result is not a whole number, 38 is not divisible by 4.
Question 3: If there are 38 cupcakes and 19 students, how many cupcakes per student?
Step 1: 38 ÷ 19 = 2
So, each student gets 2 cupcakes.
Quick Reference – Nearby Numbers’ Factors
Learning factors for numbers near 38 strengthens your understanding. Check out:
Factors of 36 | Factors of 39 | Factors of 35Practice Problems
- List all factors of 38.
- Is 38 a perfect number?
- What are the prime factors of 38?
- Write the factor pairs of 38.
- Find all common factors of 38 and 24.
Common Mistakes to Avoid
- Mixing up factors and multiples of 38.
- Missing factor pairs (especially 2 × 19).
- Assuming that all even numbers are prime.
- Not checking division results for whole numbers.
Real-World Applications
The concept of factors of 38 appears in distributing items evenly, calculating group divisions, and organizing objects in rows and columns. It helps in solving scheduling, packaging, banking, and resource-sharing problems. Vedantu supports learners in connecting such maths concepts with real-life uses.
Summary of Factors of 38
We explored the concept of factors of 38, found their list, pairs, did prime factorization, solved related problems, and saw real-world examples. Practice more with Vedantu to strengthen your understanding and boost your maths confidence!
Related Topics – Keep Learning!
Continue building your knowledge on similar math concepts:
FAQs on Factors of 38 Explained with Simple Steps and Examples
1. What are the factors of 38?
The factors of 38 are the numbers that divide 38 exactly without leaving a remainder. They are: 1, 2, 19, and 38. These factors help in understanding divisibility and prime factorization concepts for exams.
2. What is the prime factorization or factor tree of 38?
The prime factorization of 38 is found by breaking 38 into prime numbers that multiply to give 38. Using a factor tree: 38 ÷ 2 = 19, and 19 is prime. So, the prime factors are 2 × 19.
3. Is 38 a perfect number?
No, 38 is not a perfect number. A perfect number is equal to the sum of its factors (excluding itself). The factors of 38 are 1, 2, 19, and 38; their sum excluding 38 is 22, which is less than 38, so it is a deficient number.
4. What are the pairs of factors of 38?
The pairs of factors of 38 are combinations of two numbers that multiply to get 38. These are (1, 38) and (2, 19). Understanding factor pairs helps in visual learning and quick factorization.
5. Which numbers is 38 divisible by?
38 is divisible by its factors: 1, 2, 19, and 38. This means dividing 38 by any of these leaves no remainder. Divisibility rules help students verify factors quickly.
6. Is 38 a factor of 19?
No, 38 is not a factor of 19 because factors must be less than or equal to the number in question. Since 38 is greater than 19, it cannot divide 19 exactly.
7. What are the common factors of 34 and 38?
The common factors of 34 and 38 are the numbers that divide both completely. Factors of 34 are 1, 2, 17, and 34; factors of 38 are 1, 2, 19, and 38. The common factors are 1 and 2.
8. Why does 38 have only four factors?
38 has only four factors because it is a product of two prime numbers, 2 and 19. Numbers that are the product of two distinct primes usually have exactly four factors: 1, the two primes, and the number itself.
9. Why do students confuse factors with multiples of 38?
Students often confuse factors and multiples because both relate to division and multiplication. Factors divide the number exactly, whereas multiples are the results of multiplying the number by integers. Clear examples help avoid this confusion.
10. Why is factorization by division method easy for 38?
The division method is easy for 38 because it has small prime factors (2 and 19). Since 2 is the smallest prime, dividing 38 by 2 simplifies the factorization process in straightforward steps.
11. What is the sum and average of the factors of 38?
The factors of 38 are 1, 2, 19, and 38. Their sum is 1 + 2 + 19 + 38 = 60. The average is the sum divided by the number of factors, 60 ÷ 4 = 15. These calculations are important for exam problems.
12. Can factors of -38 be considered?
Yes, the factors of -38 are the negative counterparts of the factors of 38. They are -1, -2, -19, and -38, because dividing -38 by these numbers results in an integer.
