Factors of 169 Using Prime Factorization
What are the Factors of 169?
The factors of 169 are natural numbers that divide it completely. Alternatively, we can view factors of 169 as numbers that can be multiplied by another number to get 169 as the product. We won’t get a remainder if we divide 169 by any of its factors. On the other hand, we will get a remainder if we divide 169 by a number that is not its factor. The factors of 169 are listed in the given table.
Factors | Factor Pairs | Prime Factorization |
|---|---|---|
1, 13, 169 | (1, 169), (13, 13) | 169 = 13 x 13 |
List of Factors
Divisibility rules and division facts can be used to obtain the factors of 169.
Number | Is the number a factor of 169 | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of all numbers. | 1 \( \times\) 169 = 169 |
2 | No, 169 is not even | —--- |
3 | No, 1 + 6 + 9 = 16 is not divisible by 3 | —--- |
4 | No, 169 \( \div\) 4 = 42 Remainder = 1 | —--- |
5 | No, the ones digit is neither 0 nor 5. | —--- |
6 | No, 169 is not even and also not divisible by 3. | —--- |
7 | No, 169 \( \div\) 7 = 24 and Remainder = 1 | —--- |
8 | No, 169 \( \div\) 8 = 21 and Remainder = 1 | —--- |
9 | No, 169 \( \div\) 9 = 18 and Remainder = 7 | —--- |
10 | No, 169 \( \div\) 10 = 16 and Remainder = 9 | —--- |
11 | No, 169 \( \div\) 11 = 15 and Remainder = 4 | —--- |
12 | No, 169 \( \div\) 12 = 14 Remainder = 1 | —--- |
13 | Yes 169 \( \div\) 13 = 13 Remainder = 0 | 13 \( \times\) 13 = 169 |
We can stop the derivation of factors with this step because the multiplication equations will start to repeat. Hence, the factors of 169 are the multiplicands of each multiplication equation. Since there are 2 multiplication equations with unique multiplicands, the number 169 has three factors, which are, 1, 13 and 169.
Prime Factorization of 169
Prime factorization implies that we express a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of the original number.
The factor tree of 169 below represents the prime factorization of 169.
So, the prime factorization of 169 is 13 \( \times\) 13 and the prime factor of 169 is 13.
Read More:
Factor Pairs of 169
A factor pair of 169 is a set of any of its two factors when multiplied result in 169 as the product. The factor pairs of a number can be written from the list of factors of that specific number.
The factor pairs of 169 are listed as in the table.
Factors of 169 | Factor pairs of 169 |
|---|---|
1 \( \times\) 169 = 169 | (1 , 169) |
13 \( \times\) 13 = 169 | (13 , 13) |
Solved Factors of 169 Examples
Example 1: Find the common factors of 169 and 24.
Solution:
The factors of 169 are 1, 13, 169.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
Hence, the common factor of 169 and 24 is 1.
Example 2: Find the greatest common factor of 169 and 26.
Solution:
The factors of 169 are 1, 13, 169.
The factors of 26 = 1, 2, 13, 26.
Therefore, the greatest common factor of 169 and 26 is 13.
Example 3: Rex distributed 169 chocolates to all the students in his class. How many chocolates did each student get if there are 13 students in the class?
Solution:
Total number of chocolates = 169
Total number of students in class = 13
To find the number of chocolates that each student received, we just need to know the factor pair of 169 that includes 13. The factor pair is (13, 13).
Therefore, each student got 13 chocolates.
The negative factor pairs of 169 are (-1, -169) and (-13, -13).
From the factor pairs of 169 we know that 169 = 13 x 13. So the square root of 169 is 13 which is an integer. So 169 is a perfect square number.
The prime factorization of 169 is 13 x 13.
169 has more than two factors. This means that 169 is not a prime number.