Factors of 169
The factors of 169 are the whole numbers that divide 169 exactly, leaving no remainder. These numbers always come in pairs, like (1, 169) or (-1, -169), and both positive and negative factors are possible. Factors are always integers, not fractions or decimals. You can find them through simple division or prime factorization. Understanding the factors of 169 builds a strong base in number theory and helps in learning divisibility, multiples, and prime numbers. In this article, we’ll explore all positive factors, factor pairs, and the prime factorization of 169with examples to make it easy to follow.
What are the Factors of 169?
The factors of 169 are the whole numbers that divide it exactly without leaving a remainder. These numbers are 1, 13 and 169. When we include negative values, the complete set becomes -1, -13 and -169. Each of these numbers can multiply with another to give 169. In mathematics, factors help us understand how a number is built, whether it’s made up of smaller numbers or stands alone as a prime. 169 can be divided by other numbers besides 1 and itself, so it’s considered a composite number.
Factors of 169: 1, 13 and 169
Factor Pairs of 169
The factor pairs of 169 are combinations of two integers that multiply together to give exactly 169. Each pair shows how 169 can be expressed as a product of two whole numbers. The positive factor pairs are (1, 169), (13, 13), while the negative pairs are (-1, -169), (-13, -13). Learning these helps build a strong foundation in multiplication and division, and also supports understanding key concepts like the greatest common factor and prime factorization. You can also explore how factor pairs relate to the greatest common factor and prime factorization for deeper understanding.
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
Prime factorization of 169 is the process of expressing it as a product of its prime numbers. When we repeatedly divide 169 by the smallest possible prime numbers, we get 13, 13. Therefore, the prime factorization of 169 is 13^2. Knowing prime factors is essential for solving problems involving GCF, LCM, and simplifying fractions.
Prime factors of 169:
13, 13
Prime factorization of 169:
13 × 13
Compact form:
132
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How to Find the Factors of 169?
Finding the factors of 169 can be done efficiently using the division method. You only need to check numbers up to the square root of 169, because each divisor below the square root has a matching pair above it. Each number that divides 169 evenly forms a factor pair, giving you both the divisor and its corresponding factor. This method saves time and helps understand the structure of 169 in terms of its building blocks.
Optimized steps to find factors of 169:
- •169 ÷ 1 = 169 → ✅ Factor Pair: (1, 169)
- •169 ÷ 13 = 13 → ✅ Factor
This method avoids unnecessary checks and quickly identifies all factor pairs, making it especially helpful for larger numbers.
Find factors and factor pairs 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.