156 LearnersLast updated on May 26th, 2025
Factors of 469
Factors of 469 are numbers that can divide 469 completely without any remainder. We often use factors in tasks like organizing data or solving mathematical problems. In this topic, we will explore the factors of 469 and the different methods to find them.
What are the Factors of 469?
The factors of 469 are 1, 7, 67, and 469.
Positive Factors: These are positive numbers that divide 469 completely.
Positive factors: 1, 7, 67, 469
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -7, -67, -469
Prime Factors: Prime factors are the prime numbers that, when multiplied together, give 469 as the product.
Prime factors: 7, 67
Prime Factorization: Prime factorization involves breaking 469 into its prime factors.
It is expressed as 71 × 671
Table Listing the Factors of 469
|
Positive Factors |
1, 7, 67, 469 |
| Negative Factors |
-1, -7, -67, -469 |
|
Prime Factors |
7, 67 |
|
Prime Factorization |
71 × 671 |
This breakdown helps in understanding the various factors of 469, whether they are positive or negative, as well as how prime factorization works for this number.
Finding Factors Using the Multiplication Method
The multiplication method finds the pair of factors that give 469 as their product.
Step 1: Find the pair of numbers whose product is 469.
Step 2: The factors are those numbers that, when multiplied, give 469.
Make a list of numbers whose product will be 469.
List of Numbers:
- 1 × 469 = 469
- 7 × 67 = 469
Thus, the factors of 469 are 1, 7, 67, and 469.
Finding Factors Using the Division Method
The division method identifies numbers that divide 469 completely.
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 469÷1=469.
Step 2: Move to the next integers. Include numbers that divide 469 completely.
Thus, the factors of 469 are 1, 7, 67, and 469.
Prime Factors and Prime Factorization
Prime Factors: Prime factors are prime numbers that give the product of 469.
Prime factors of 469: 7, 67
Prime Factorization: Prime factorization involves dividing 469 into its prime factors.
Step 1: Divide 469 by the smallest prime number, 7.
469÷7=67
Step 2: 67 is already a prime number.
Prime Factorization of 469: 71 × 671
Factor Tree
The prime factorization can be visually represented using a factor tree.
This tree shows the breakdown of 469 into its prime factors: 7×67.
In this factor tree, each branch splits into prime factors.
Factors of 469 in Positive and Negative Pairs
Factors of 469 can be expressed in both positive and negative pairs. Their product equals the given number.
Positive Factor Pairs: (1, 469), (7, 67)
Negative Factor Pairs: (-1, -469), (-7, -67)
Common Mistakes and How to Avoid Them in Factors of 469
Mistakes can occur while finding the factors. Learn about the common errors that can occur. Solutions to solve the common mistakes are given below:
Mistake 1
Assuming 7 as the only factor of 469.
Since 7 divides 469, one may assume it's the only factor. Remember, factors are numbers that divide completely. Other factors include 1, 67, and 469.
Factors of 469 Examples
Problem 1
Identify the factors of 469
The factors of 469 are 1, 7, 67, and 469
Explanation
The factors of a number are the integers that divide the number without leaving a remainder. When you divide 469 by 1, 7, 67, and 469, there is no remainder, confirming these are its factors.
Problem 2
Identify the perfect square from the factors of 469
There are no perfect square factors of 469
Explanation
A perfect square is a number we get when the same number is multiplied twice. None of the factors of 469 (1, 7, 67, 469) form a perfect square when multiplied by themselves.
Problem 3
Can you check whether 7 and 67 are co-prime?
Yes, 7 and 67 are co-prime
Explanation
To check whether the two numbers are co-prime, list their factors and determine the GCF. If the GCF is 1, then the numbers are co-prime.
Factors of 7: 1, 7
Factors of 67: 1, 67
Here, the GCF is 1. So, 7 and 67 are co-prime. For co-prime numbers, the GCF should be 1.
Problem 4
Verify whether 47 is a multiple of 23
Yes, 47 is not a multiple of 23
Explanation
Multiples of 23 are numbers we get when 23 is multiplied by another number. No number can be multiplied by 23 to get 47 as the product.
Problem 5
Can you check whether 15 and 31 are co-prime?
Yes, 15 and 31 are co-prime.
Explanation
To check whether the 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 greater than 1, then the numbers are not co-prime.
Factors of 15: 1, 3, 5, 15
Factors of 31: 1, 31
Here, the GCF is 1. So, 15 and 31 are co-prime. For co-prime numbers, the GCF should be 1.
FAQs on Factors of 469
1.What are the factors of 469?
2.How do you determine if a number is a factor of 469?
3.What is the smallest factor of 469?
4.What is the largest factor of 469?
5.How many factors does 469 have?
6.How many odd factors does 469 have?
7.What factors go into 469?
8.Do any perfect squares exist in the factors of 469?
Important glossaries for the Factors of 469
- Factors: Numbers that can divide a given number completely without leaving a remainder.
- Prime Factors: Prime numbers that multiply together to give the original number.
- Prime Factorization: The process of expressing a number as the product of its prime factors.
- Factor Tree: A diagram used to break down a number into its prime factors, visually representing the factorization process.
- Multiple: A number that results when a given number is multiplied by an integer.
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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.
