191 LearnersLast updated on May 26th, 2025
Factors of 390
Factors of 390 are numbers that can divide 390 completely without leaving a remainder. We often use factors for various practical applications, such as organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 390 and the different methods to find them.
What are the Factors of 390?
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
Positive Factors: These are the positive numbers that divide 390 evenly. Positive factors: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
Negative Factors: These are the negative counterparts of the positive factors. Negative factors: -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -195, -390
Prime Factors: Prime factors are the prime numbers themselves, when multiplied together, give 390 as the product. Prime factors: 2, 3, 5, 13
Prime Factorization: Prime factorization involves breaking 390 into its prime factors. It is expressed as: 390=2×3×5×13
How to Find the Factors of 390?
There are various methods to find the factors of 390:
Methods to Find the Factors of 390:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
This breakdown helps in understanding the various factors of 390, whether they are positive or negative, and how prime factorization works for this number.
Finding Factors Using Multiplication
The multiplication method identifies pairs of numbers whose product is 390.
Step 1: Find pairs of numbers whose product equals 390.
Step 2: The factors are those numbers that, when multiplied, give 390.
Step 3: List the pairs of numbers whose product equals 390. A list of pairs whose product is 390 is given below:
- 1 × 390 = 390
- 2 × 195 = 390
- 3 × 130 = 390
- 5 × 78 = 390
- 6 × 65 = 390
- 10 × 39 = 390
- 13 × 30 = 390
- 15 × 26 = 390
Thus, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are outlined below:
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 390÷1=390390 \div 1 = 390390÷1=390
Step 2: Move to the next integer. The factors of 390 include the number used to divide and the quotient obtained.
Thus, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
Prime Factors and Prime Factorization
Prime factors of 390 are obtained by dividing the number by its prime numbers. A number simplified using its prime factors and expressed in the form of prime factorization is the prime factorization of that number.
Prime Factors of 390: 2, 3, 5, 13 Prime Factorization of 390:
Divide 390 by 2: 390÷2=195
Divide 195 by 3: 195÷3=65
Divide 65 by 5: 65÷5=13
Divide 13 by 13: 13÷13=1
Prime factorization of 390: 2×3×5×13
Factor Tree
The prime factorization of 390 can be visually represented using a factor tree. This helps in understanding how the number is broken down into its prime factors.
Factors of 390 in Pairs
Factors of 390 can be written in both positive and negative pairs. Their product will be equal to 390.
Positive Factor Pairs: (1, 390), (2, 195), (3, 130), (5, 78), (6, 65), (10, 39), (13, 30), (15, 26)
Negative Factor Pairs: (-1, -390), (-2, -195), (-3, -130), (-5, -78), (-6, -65), (-10, -39), (-13, -30), (-15, -26)
Common Mistakes and How to Avoid Them in Factors of 390
Mistakes can occur while finding the factors. Here are common errors and how to avoid them
Mistake 1
Assuming 2 or 5 as the only prime factors of 390.
Remember that 390 can be divided by other numbers as well, such as 3 and 13. Always verify the complete set of factors.
Factors of 390 Examples
Problem 1
Can you check whether 15 and 26 are co-prime?
Yes, 15 and 26 are co-prime.
Explanation
To check whether two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is 1, then the numbers are co-prime.
Factors of 15: 1, 3, 5, 15
Factors of 26: 1, 2, 13, 26
Here, the GCF is 1. So, 15 and 26 are co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 78 is a multiple of 13
Yes, 78 is a multiple of 13.
Explanation
Multiples of 13 are numbers we get when 13 is multiplied by another number. 13 × 6 = 78, which confirms that 78 is a multiple of 13.
Problem 3
Identify the perfect square from the factors of 390
The perfect square factor of 390 is 1.
Explanation
A perfect square is a number we get when the same number is multiplied twice. In the factors of 390, only 1 is a perfect square because it is 1 × 1.
Problem 4
What are the factors of 390?
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, and 390.
Explanation
To find the factors of 390, we look for all numbers that divide 390 evenly without leaving a remainder. The complete list includes all such divisors.
Problem 5
Are 30 and 78 co-prime?
No, 30 and 78 are not co-prime.
Explanation
To determine if two numbers are co-prime, we must check their GCF. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78 The GCF of 30 and 78 is 6, which is greater than 1. Hence, they are not co-prime.
FAQs on Factors of 390
1.What are the factors of 390?
2.How do you determine if a number is a factor of 390?
3.What is the smallest factor of 390?
4.What is the largest factor of 390?
5.How many factors does 390 have?
6.How many odd factors does 390 have?
7.What factors go into 390?
8.Do any perfect squares exist in the factors of 390?
9.How can children in India use numbers in everyday life to understand Factors of 390?
10.What are some fun ways kids in India can practice Factors of 390 with numbers?
11.What role do numbers and Factors of 390 play in helping children in India develop problem-solving skills?
12.How can families in India create number-rich environments to improve Factors of 390 skills?
Important glossaries for the Factors of 390
- Co-prime: Numbers having 1 as the only common factor. For example, 15 and 26 are co-prime because their greatest common factor (GCF) is 1.
- Perfect Square: The number we get when the same number is multiplied twice. For example, 1 is a perfect square because it is 1×1
- Prime Factors: Prime numbers that, when multiplied together, give a specific number as the product. For 390, the prime factors are 2, 3, 5, and 13.
- Factor Tree: A tree diagram used to represent the prime factors of a given number. It helps visualize how a number is broken down into its prime factors.
- Multiple: Numbers we get when another number multiplies the given number. For example, 78 is a multiple of 13 because 13×6=78
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About BrightChamps in India
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
