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.
 

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
   

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).
 

• 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.