Factors of 248
The factors of 248 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 248) or (-1, -248), 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 248, including all positive factors, factor pairs, and the prime factorization of 248 with step-by-step explanations and examples.
What are the Factors of 248?
There are 8 factors of 248. The factors of 248 are 1, 2, 4, 8, 31, 62, 124 and 248. Factors can be negative. The negative factors are -1, -2, -4, -8, -31, -62, -124 and -248. All of these numbers divides 248 completely. 248 is a composite number because it has other factors besides 1 and 248.
Factors of 248: 1, 2, 4, 8, 31, 62, 124 and 248
Factor Pairs of 248
The factor pairs of 248 are the pairs of integers that multiply together to give 248. These include both positive and negative combinations. The positive factor pairs of 248 are (1, 248), (2, 124), (4, 62), (8, 31), and the negative factor pairs are (-1, -248), (-2, -124), (-4, -62), (-8, -31). Knowing the factor pairs of 248 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 248:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 248 |
| 2 | 124 |
| 4 | 62 |
| 8 | 31 |
Negative Factor Pairs of 248:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -248 |
| -2 | -124 |
| -4 | -62 |
| -8 | -31 |
Prime Factorization of 248
The prime factorization of 248 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 248 are 2, 2, 2, 31. Therefore, the prime factorization of 248 is 2^3 × 31. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 248:
2, 2, 2, 31
Prime factorization of 248:
2 × 2 × 2 × 31
Compact form:
23 × 31
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How to Find the Factors of 248?
To find the factors of 248 using the division method efficiently, you only need to check numbers up to the square root of 248. For every number that divides 248 evenly, both it and its corresponding pair (248 ÷ that number) are factors.
Optimized steps to find factors of 248:
- •248 ÷ 1 = 248 → ✅ Factor Pair: (1, 248)
- •248 ÷ 2 = 124 → ✅ Factor Pair: (2, 124)
- •248 ÷ 4 = 62 → ✅ Factor Pair: (4, 62)
- •248 ÷ 8 = 31 → ✅ Factor Pair: (8, 31)
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 248
What are the factors of 248?
The factors of 248 are 1, 2, 4, 8, 31, 62, 124, 248.
What is the prime factorization of 248?
The prime factorization of 248 is 2 × 2 × 2 × 31.
How do I find the factors of 248?
To find the factors of 248, start by dividing 248 by every number from 1 up to the square root of 248.
What are factor pairs of 248?
The factor pairs of 248 are (1, 248), (-1, -248), (2, 124), (-2, -124), (4, 62), (-4, -62), (8, 31), (-8, -31).
How can I use the factors of 248?
The factors of 248 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 248 always positive?
Factors can be both positive and negative. For example, the negative factors of 248 are -1, -2, -4, -8, -31, -62, -124, -248.