Factors of 700
When we talk about the factors of 700, we mean the whole numbers that divide 700 exactly. They are the building blocks of 700 and always come in matching pairs, one small and one large, like (1, 700). Factors never include fractions or decimals. You can find them by dividing 700 by smaller integers until the division is exact. Understanding the factors of 700 makes it easier to learn about primes, multiples, and greatest common divisors. In this guide, we’ll show the list of all positive factors, factor pairs, and the prime factorization of 700 in an easy-to-read format.
What are the Factors of 700?
The list of factors for 700 shows which numbers divide it evenly. These positive factors are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350 and 700, and the negative ones are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350 and -700. Each factor reveals something about the structure of 700. Factors are used in many areas of math from simplifying fractions to finding greatest common divisors. 700 turns out to be a composite number since it’s divisible by more than just 1 and itself.
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
Factor pairs show how a number can be broken down into two smaller factors that multiply to form it. For 700, these pairs are (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35), (25, 28) on the positive side and (-1, -700), (-2, -350), (-4, -175), (-5, -140), (-7, -100), (-10, -70), (-14, -50), (-20, -35), (-25, -28) on the negative side. They are an important part of basic number theory and help explain multiplication, division, and factorization in a simple way. Knowing the factor pairs of 700 can make it easier to find related values such as the greatest common factor or least common multiple. You can also explore how factor pairs relate to the greatest common factor and prime factorization for deeper understanding.
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
To understand 700 more deeply, we can decompose it into its prime factors. By dividing step by step, we find that 700 can be written as 2 × 2 × 5 × 5 × 7. Hence, the prime factorization of 700 is 2^2 × 5^2 × 7. Prime factorization is an important concept in arithmetic and algebra because it helps in computing the LCM, greatest common factor, and simplifying complex 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?
The most effective way to find factors of 700 is to divide it by numbers up to its square root. Each divisor provides a matching factor, forming a pair that multiplies back to 700. This method not only finds all factors efficiently but also helps you understand the relationships between numbers. It's a practical way to explore factorization and basic arithmetic properties.
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 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 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.