Factors of 700
The factors of 700 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 700) or (-1, -700), 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 700, including all positive factors, factor pairs, and the prime factorization of 700 with step-by-step explanations and examples.
What are the Factors of 700?
There are 18 factors of 700. The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350 and 700. Factors can be negative. The negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350 and -700. All of these numbers divides 700 completely. 700 is a composite number because it has other factors besides 1 and 700.
Factors of 700: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350 and 700
Factor Pairs of 700
The factor pairs of 700 are the pairs of integers that multiply together to give 700. These include both positive and negative combinations. The positive factor pairs of 700 are (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35), (25, 28), and the negative factor pairs are (-1, -700), (-2, -350), (-4, -175), (-5, -140), (-7, -100), (-10, -70), (-14, -50), (-20, -35), (-25, -28). Knowing the factor pairs of 700 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 700:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 700 |
| 2 | 350 |
| 4 | 175 |
| 5 | 140 |
| 7 | 100 |
| 10 | 70 |
| 14 | 50 |
| 20 | 35 |
| 25 | 28 |
Negative Factor Pairs of 700:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -700 |
| -2 | -350 |
| -4 | -175 |
| -5 | -140 |
| -7 | -100 |
| -10 | -70 |
| -14 | -50 |
| -20 | -35 |
| -25 | -28 |
Prime Factorization of 700
The prime factorization of 700 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 700 are 2, 2, 5, 5, 7. Therefore, the prime factorization of 700 is 2^2 × 5^2 × 7. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 700:
2, 2, 5, 5, 7
Prime factorization of 700:
2 × 2 × 5 × 5 × 7
Compact form:
22 × 52 × 7
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 700?
To find the factors of 700 using the division method efficiently, you only need to check numbers up to the square root of 700. For every number that divides 700 evenly, both it and its corresponding pair (700 ÷ that number) are factors.
Optimized steps to find factors of 700:
- •700 ÷ 1 = 700 → ✅ Factor Pair: (1, 700)
- •700 ÷ 2 = 350 → ✅ Factor Pair: (2, 350)
- •700 ÷ 4 = 175 → ✅ Factor Pair: (4, 175)
- •700 ÷ 5 = 140 → ✅ Factor Pair: (5, 140)
- •700 ÷ 7 = 100 → ✅ Factor Pair: (7, 100)
- •700 ÷ 10 = 70 → ✅ Factor Pair: (10, 70)
- •700 ÷ 14 = 50 → ✅ Factor Pair: (14, 50)
- •700 ÷ 20 = 35 → ✅ Factor Pair: (20, 35)
- •700 ÷ 25 = 28 → ✅ Factor Pair: (25, 28)
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 700
What are the factors of 700?
The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.
What is the prime factorization of 700?
The prime factorization of 700 is 2 × 2 × 5 × 5 × 7.
How do I find the factors of 700?
To find the factors of 700, start by dividing 700 by every number from 1 up to the square root of 700.
What are factor pairs of 700?
The factor pairs of 700 are (1, 700), (-1, -700), (2, 350), (-2, -350), (4, 175), (-4, -175), (5, 140), (-5, -140), (7, 100), (-7, -100), (10, 70), (-10, -70), (14, 50), (-14, -50), (20, 35), (-20, -35), (25, 28), (-25, -28).
How can I use the factors of 700?
The factors of 700 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 700 always positive?
Factors can be both positive and negative. For example, the negative factors of 700 are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350, -700.