165 LearnersLast updated on May 26th, 2025
Factors of 237
Factors of 237 are numbers that can divide 237 completely without leaving a remainder. We often use factors in various ways, such as organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 237 and the different methods to find them.
What are the Factors of 237?
The factors of 237 are 1, 3, 79, and 237.
Positive Factors: These are the factors that can divide 237 completely and are positive numbers.
Positive factors: 1, 3, 79, 237
Negative Factors: These are the negative counterparts of the positive factors.
Negative factors: -1, -3, -79, -237
Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 237 as the product.
Prime factors: 3, 79
Prime Factorization:Prime factorization involves breaking down 237 into its prime factors. It can be expressed as:
Prime factorization: 3 × 79
How to Find the Factors of 237?
There are different methods to find the factors of 237.
Methods to find the factors of 237:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
This breakdown helps in understanding the various factors of 237, whether they are positive or negative, as well as how prime factorization works for this number.
Finding Factors Using the Multiplication
The multiplication method finds pairs of factors that, when multiplied, give 237 as their product.
Step 1: Find the pair of numbers whose product is 237.
Step 2: The factors are those numbers that, when multiplied, give 237.
Step 3: Make a list of numbers whose product will be 237.
- 1 × 237 = 237
- 3 × 79 = 237
Thus, the factors of 237 are 1, 3, 79, and 237.
Finding Factors Using the Division Method
The division method finds numbers that fully divide 237.
Step 1: Since every number is divisible by 1, 1 is always a factor. Example: 237 ÷ 1 = 237
Step 2: Move to the next integer. The factors of 237 include the number used to divide and the quotient.
Step 3: List the factors.
Factors of 237: 1, 3, 79, and 237.
Prime Factors and Prime Factorization
Prime factors of a number are the prime numbers that multiply to give that number. Prime factorization is the process of expressing a number as the product of its prime factors.
Prime Factors of 237: The prime factors of 237 are 3 and 79.
Finding Prime Factors of 237:
- Divide 237 by the prime number 3.
237 ÷ 3 = 79
- Divide 79 by the prime number 79.
79 ÷ 79 = 1
Prime Factorization of 237: 3 × 79
Factor Tree
The prime factorization can also be visually represented using a factor tree. This method helps to understand the breakdown easily.
Factor Tree for 237: This tree shows the breakdown of 237 into its prime factors: 3 × 79.
Positive and Negative Factor Pairs of 237
Factors of 237 can be written as both positive and negative pairs. They are like team members, and their product will be equal to the given number.
Positive Factor Pairs: (1, 237), (3, 79)
Negative Factor Pairs: (-1, -237), (-3, -79)
Common Mistakes and How to Avoid Them in Factors of 237
Mistakes can occur while finding factors. Here are some common errors and solutions:
Mistake 1
Assuming 79 is not a factor of 237.
Verify by dividing 237 by 79. If it divides completely without a remainder, then 79 is a factor
Factors of 237 Examples
Problem 1
Can you check whether 237 and 9 are co-prime?
Yes, 237 and 9 are co-prime
Explanation
To check if two numbers are co-prime, list their factors and find their greatest common factor (GCF).
Factors of 237: 1, 3, 79, 237
Factors of 9: 1, 3, 9
Here, the GCF is 3. Since the GCF is greater than 1, 237 and 9 are not co-prime.
Problem 2
Verify whether 237 is a multiple of 3
Yes, 237 is a multiple of 3
Explanation
To determine if 237 is a multiple of 3, divide 237 by 3.
237 ÷ 3 = 79, which is an integer. This confirms that 237 is divisible by 3, making it a multiple of 3.
Problem 3
Identify the perfect square from the factors of 237
The perfect square factor of 237 is 1
Explanation
A perfect square is a number that results from multiplying a number by itself. The only perfect square in the factors of 237 is 1 (1 × 1).
Problem 4
Are the factors of 237 all prime?
No, not all factors of 237 are prime
Explanation
The factors of 237 are 1, 3, 79, and 237. Among these, 3 and 79 are prime numbers, but 1 and 237 are not prime.
Problem 5
What are the factors of 237?
The factors of 237 are 1, 3, 79, and 237
Explanation
Factors are numbers that divide 237 without leaving a remainder. The complete set of factors for 237 is 1, 3, 79, and 237.
FAQs on Factors of 237
1.What are the factors of 237?
2.How do you determine if a number is a factor of 237?
3.What is the smallest factor of 237?
4.What is the largest factor of 237?
5.How many factors does 237 have?
6.How many odd factors does 237 have?
7.What factors go into 237?
8.Do any perfect squares exist in the factors of 237?
Important glossaries for the Factors of 237
- Factors: Numbers that can divide a given number completely without leaving a remainder.
- Prime Factors: Prime numbers that multiply together to give a specific number.
- Prime Factorization: Expressing a number as the product of its prime factors.
- Multiple: A number that is the product of a given number and an integer.
- Perfect Square: A number that results from multiplying an integer by itself.
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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.
