167 LearnersLast updated on May 26th, 2025
Factors Of 169
In mathematics, there are lots of numbers that when divided by other numbers leave no remainder, these numbers are called factors. We use it in our vehicles mileage and money handling. Now, we’ll learn what factors are and factors of 169 let us now see.
Factors Of 169
We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 169 has more than 2 factors. Let us find what the factors are.
Negative factors of 169: -1, -13 and -169.
Prime factors of 169: The prime factors of 169 is 13.
Prime factorization of 169: 13×13
The sum of factors of 169: 1+13+169= 183.
How to find the factors of 169
Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 169.
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
Finding The Factors Of 169 Using Multiplication
In the multiplication method, we find pairs of numbers where the product will be 169. In this process, possible steps will be -
Step 1: Find all those numbers whose product will be 169.
Step 2: These numbers will be called the factors of 169.
Step 3: Students have to write these pairs of numbers for this method.
List of numbers whose product is 169
169×1= 169
13×13= 169
So the pair of numbers whose product is 169 are (1,169) and (13,13)
Finding Factors Using Division Method
For the division method, the process of division will go on until the remainder becomes zero.
Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 169÷1 = 169.
Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 169÷13 = 13 and so on.
Prime Factorization And Prime Factors
Prime factorization is the process where the number will be a product of prime factors or prime numbers.
Prime Factors Of 169: The prime factors of 169 is 13. We find the prime factors of 169 by two ways.
Prime Factorization:Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 169, the steps are like this:
169/13= 13
13/13= 1
As 13 is a prime number, it is only divisible by 13. Hence, The prime factorization of the number 169 is 13×13.
Factor Tree:
This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.
Step 1: 169 divided by 13 gives us the answer being 13.
Step 2: 13 divided by 13 gives us 1.
Step 4: This we can’t divide further.
Factor Pairs For 169
There are positive and negative factor pairs for a given number. Let us look at these factor pairs.
Positive Factor Pairs: (1,169) and (13,13).
Negative Factor Pairs: (-1,-169) and (-13,-13).
Common mistakes and how to avoid them in the factors of 169
It is very normal to make mistakes when learning to find the factors. Here are the commonly made mistakes by children. Avoid these when practicing!
Mistake 1
Assuming 169 is prime,
One may wrongly assume that the number 169 is prime and stop looking for factors.
Factors Of 169 Examples
Problem 1
Let us look at some of the examples that are related to factors and how to solve them.
A rectangular garden has an area of 169 square meters. If the length of the garden is 13 meters, what is the width?
Explanation
The width is 13 meters, as Area=Length×Width and 169=13×Width, so Width = 13 meters.
Explanation: The area of a rectangle is length times width. So, 169 = 13 × width, and width = 13 meters.
Problem 2
If a square has a side length of 13 units, what is its area?
The area of the square is 169 square units, as Area=side2, so 132=169.
Explanation
The area is found by multiplying the side length by itself. Here, 13 × 13 = 169 square units.
Problem 3
A square table has an area of 169 square inches. If its side length is increased by 2 inches, what is the new area?
The new area is 225 square inches, as the new side length is 13+2=15, and 152=225.
Explanation
The side length is 15 inches (13+2). Multiply 15 by 15 to get the new area: 225.
.
Problem 4
A rectangle’s length is 13 meters, and its area is 169 square meters. What is its width?
The width of the rectangle is 13 meters, as Area=Length×Width, so 169=13×Width, so Width = 13 meters.
Explanation
The area of a rectangle is length times width. Since 169 = 13 × width, width = 13 meters.
Problem 5
A book has 169 pages. If a person reads 13 pages per day, how many days will it take to finish the book?
It will take 13 days to finish the book, as 169÷13=13.
Explanation
If you read 13 pages each day, dividing 169 pages by 13 gives 13 days to complete the book.
FAQs For Factors Of 169
1.What are the factors of 169?
2.How many factors does the number 169 have, and what are they?
3.What are the prime factors of 169, and what is its prime factorization?
4.Is 169 divisible by other numbers besides 1, 13, and 169?
5.What two identical numbers multiply together to make 169?
6.How can children in United Kingdom use numbers in everyday life to understand Factors Of 169?
7.What are some fun ways kids in United Kingdom can practice Factors Of 169 with numbers?
8.What role do numbers and Factors Of 169 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors Of 169 skills?
Important Glossaries for Factors of 169
- Multiplication Method: It is a technique by which factors of a number are located by pairing and verifying the numbers, which product is the original number.
- Perfect Square: A number that is the product of a whole number multiplied by itself. 169 is a perfect square (13 × 13).
- Factor Tree: A diagram that breaks down a number into its prime factors by dividing it progressively, like 169 divided by 13.
- Prime Factors: The numbers that the prime numbers multiply to equals to the actual number. 169 is the prime factor of 13.
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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.
