Last updated on May 26th, 2025
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.
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.
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.
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)
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 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.
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.
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).
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!
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?
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.
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.
The area is found by multiplying the side length by itself. Here, 13 × 13 = 169 square units.
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.
The side length is 15 inches (13+2). Multiply 15 by 15 to get the new area: 225.
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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.
The area of a rectangle is length times width. Since 169 = 13 × width, width = 13 meters.
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.
If you read 13 pages each day, dividing 169 pages by 13 gives 13 days to complete the book.
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.
: She loves to read number jokes and games.