Factors of 169
The factors of 169 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 169) or (-1, -169), and are always integers, never fractions or decimals. You can find them using methods such as division or prime factorization. Learning about factors helps build a foundation for understanding divisibility, multiples, and prime numbers. In this guide, we'll explore the different types of factors of 169, including all positive factors, factor pairs, and the prime factorization of 169 with step-by-step explanations and examples.
What are the Factors of 169?
There are 3 factors of 169. The factors of 169 are 1, 13 and 169. Factors can be negative. The negative factors are -1, -13 and -169. All of these numbers divides 169 completely. 169 is a composite number because it has other factors besides 1 and 169.
Factors of 169: 1, 13 and 169
Factor Pairs of 169
The factor pairs of 169 are the pairs of integers that multiply together to give 169. These include both positive and negative combinations. The positive factor pairs of 169 are (1, 169), (13, 13), and the negative factor pairs are (-1, -169), (-13, -13). Knowing the factor pairs of 169 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 169:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 169 |
| 13 | 13 |
Negative Factor Pairs of 169:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -169 |
| -13 | -13 |
Prime Factorization of 169
The prime factorization of 169 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 169 are 13, 13. Therefore, the prime factorization of 169 is 13^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 169:
13, 13
Prime factorization of 169:
13 × 13
Compact form:
132
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 169?
To find the factors of 169 using the division method efficiently, you only need to check numbers up to the square root of 169. For every number that divides 169 evenly, both it and its corresponding pair (169 ÷ that number) are factors.
Optimized steps to find factors of 169:
- •169 ÷ 1 = 169 → ✅ Factor Pair: (1, 169)
- •169 ÷ 13 = 13 → ✅ Factor
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
Find factors and factors pair of any number with our Factor Checker tool.
Frequently Asked Questions about factors of 169
What are the factors of 169?
The factors of 169 are 1, 13, 169.
What is the prime factorization of 169?
The prime factorization of 169 is 13 × 13.
How do I find the factors of 169?
To find the factors of 169, start by dividing 169 by every number from 1 up to the square root of 169.
What are factor pairs of 169?
The factor pairs of 169 are (1, 169), (-1, -169), (13, 13), (-13, -13).
How can I use the factors of 169?
The factors of 169 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 169 always positive?
Factors can be both positive and negative. For example, the negative factors of 169 are -1, -13, -169.