Factors of 169
169 is the perfect square of an odd number 13, which is a prime number as well. 169 is one of the few squares for the reverse equation is also true i.e. 31 x 31 = 961. Factors of 169 are the numbers which when multiplied in pairs give the product as 169. These factors can be negative as well. 169 is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 169, prime factors of 169, and factors of 169 in pairs along with solved examples for a better understanding.
- Factors of 169: 1, 13 and 169
- Prime Factorization of 169: 13 × 13
|1.||What Are the Factors of 169?|
|2.||How to Calculate Factors of 169?|
|3.||Factors of 169 by Prime Factorization|
|4.||Factors of 169 in Pairs|
|5.||FAQs on Factors of 169|
What Are the Factors of 169?
The factor of a number is that number that divides it completely without leaving any remainder.
Therefore, to find the factors of the number 169, we will have to perform division on 169 and find the numbers which divide 169 completely.
How to Calculate the Factors of 169?
To calculate the factors of 169, we need to find all the numbers that would divide 169 without leaving any remainder. We start with the number 1, then check for numbers 2,3,4,5,6,7, and so on up to 85, (the approximate half of 169). The number 1 and the number itself would always be a factor of a given number.
Refer to the following table to check the division of 169 by its factors:
|169 ÷ 1||
Remainder = 0
Factor = 1
|169 ÷ 13||
Remainder = 0
Factor = 13
|169 ÷ 169||
Remainder = 0
Factor = 169
- Only composite numbers can have more than two factors.
- 169 is a perfect square number. Thus, it will have an odd number of factors. This property holds true for every perfect square number.
Factors of 169 by Prime Factorization
Prime Factorization of a number refers to breaking down a number into the form of products of its prime factors. There are different methods that can be used to find the factors of 169 by prime factorization.
To find the prime factors of 169 using the division method,
- Start dividing 169 by the smallest prime number, i.e., 2,3,5, and so on. Then find the smallest prime factor of the number.
- After finding the smallest prime factor of the number 169, which is 13, divide 169 by 13 to obtain the quotient 13. 169 ÷ 13 = 13
- Repeat the first step with the obtained quotient (13). Again, the prime factor for 13 would be 13. 13 ÷ 13 = 1
So, the prime factorization of 169 is 13 × 13 = 132
Factor Tree Method
We can do the same procedure using the factor tree of 169 as shown in the diagram given below.
So, the prime factorization of 169 is 13 × 13.
Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed it, for prime numbers, there are no other factors.
Factors of 169 in pairs
Pair Factors are the factors of a number given in pairs, which when multiplied together give that original number. The pair factors of 169 would be the two numbers which when multiplied together, result in the value 169
The following table represents the calculation of factors of 169 in pairs:
|Factor Pair||Pair Factorization|
|1 and 169||
1 × 169 = 169
|13 and 13||
13 × 13 = 169
Therefore, the pair factors of 169 can be listed as (1, 169) and (13, 13).
Solved Examples on factors of 169
Example 1 Calculate the sum of all the factors of 169.
The factors of 169 = 1, 13, 169
The sum of all the factors = 1 + 13 + 169 = 183
Example 2 What are the common factors of 169 and 196?
We know that,
Factors of 169 = 1, 13, 169
Factors of 196 = 1, 2, 4, 7, 14, 28, 49, 98, 196
Thus, the common factor of 169 and 196 is 1.
FAQs on factors of 169
1.What are the factors of 169?
The factors of 169 are 1, 13, and 169.
2.What is the highest factor of 169?
The highest factor of 169 is 169.
3.What are the common factors of 169 and 182?
The common factors of 169 and 182 are 1 and 13.
4.Is 169 a prime number?
No, 169 is not a prime number. It is a composite number because it has more than 2 factors: 1, 13, and 169 (the number itself).
5.Is 169 a perfect square?
The square root of 169 is 13. Hence 169 is a perfect square.