Factors of 238
The factors of 238 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 238) or (-1, -238), 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 238, including all positive factors, factor pairs, and the prime factorization of 238 with step-by-step explanations and examples.
What are the Factors of 238?
There are 8 factors of 238. The factors of 238 are 1, 2, 7, 14, 17, 34, 119 and 238. Factors can be negative. The negative factors are -1, -2, -7, -14, -17, -34, -119 and -238. All of these numbers divides 238 completely. 238 is a composite number because it has other factors besides 1 and 238.
Factors of 238: 1, 2, 7, 14, 17, 34, 119 and 238
Factor Pairs of 238
The factor pairs of 238 are the pairs of integers that multiply together to give 238. These include both positive and negative combinations. The positive factor pairs of 238 are (1, 238), (2, 119), (7, 34), (14, 17), and the negative factor pairs are (-1, -238), (-2, -119), (-7, -34), (-14, -17). Knowing the factor pairs of 238 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 238:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 238 |
| 2 | 119 |
| 7 | 34 |
| 14 | 17 |
Negative Factor Pairs of 238:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -238 |
| -2 | -119 |
| -7 | -34 |
| -14 | -17 |
Prime Factorization of 238
The prime factorization of 238 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 238 are 2, 7, 17. Therefore, the prime factorization of 238 is 2 × 7 × 17. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 238:
2, 7, 17
Prime factorization of 238:
2 × 7 × 17
Compact form:
2 × 7 × 17
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How to Find the Factors of 238?
To find the factors of 238 using the division method efficiently, you only need to check numbers up to the square root of 238. For every number that divides 238 evenly, both it and its corresponding pair (238 ÷ that number) are factors.
Optimized steps to find factors of 238:
- •238 ÷ 1 = 238 → ✅ Factor Pair: (1, 238)
- •238 ÷ 2 = 119 → ✅ Factor Pair: (2, 119)
- •238 ÷ 7 = 34 → ✅ Factor Pair: (7, 34)
- •238 ÷ 14 = 17 → ✅ Factor Pair: (14, 17)
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
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Frequently Asked Questions about factors of 238
What are the factors of 238?
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238.
What is the prime factorization of 238?
The prime factorization of 238 is 2 × 7 × 17.
How do I find the factors of 238?
To find the factors of 238, start by dividing 238 by every number from 1 up to the square root of 238.
What are factor pairs of 238?
The factor pairs of 238 are (1, 238), (-1, -238), (2, 119), (-2, -119), (7, 34), (-7, -34), (14, 17), (-14, -17).
How can I use the factors of 238?
The factors of 238 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 238 always positive?
Factors can be both positive and negative. For example, the negative factors of 238 are -1, -2, -7, -14, -17, -34, -119, -238.