Factors of 700: Prime Factorization, Methods, and Examples

The factors of 700 are the numbers that are completely divisible by the number 700. The number 700 is an even number with eighteen factors in total which is why it is called a composite number. 

Let us explore more about the factors.

Factors of 700

Here are the factors of number 700.

Factors of 700: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.

Negative Factors of 700

The negative factors of 700 are similar to its positive aspects, just with a negative sign.

Negative Factors of 700: –1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350, and -700

Prime Factorization of 700

The prime factorization of 700 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 5 x 5 x 7 

In this article, we will learn about the factors of 700 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

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, and 700. These numbers are the factors as they do not leave any remainder when divided by 700.

The factors of 700 are classified as prime numbers and composite numbers. The prime factors of the number 700 can be determined using the prime factorization technique.

How To Find the Factors of 700?

You can find the factors of 700 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 700, create a list containing the numbers divisible by 700 with zero remainders. One important thing to note is that 1 and 700 are the 700’s factors, as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 700 are determined as follows:

\[\dfrac{700}{1} = 700\]

\[\dfrac{700}{2} = 350\]

\[\dfrac{700}{4} = 175\]

\[\dfrac{700}{5} = 140\]

\[\dfrac{700}{7} = 100\]

\[\dfrac{700}{10} = 70\]

\[\dfrac{700}{14} = 50\]

\[\dfrac{700}{20} = 35\]

\[\dfrac{700}{25} = 28\]

Therefore, 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700 are the factors of 700.

Total Number of Factors of 700

For 700, there are eighteen positive factors and eighteen negative ones. So in total, there are 36 factors of 700. 

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of 700 is 1 x 2$^2$ x 5$^2$ x 7.

The exponent of 1 and 7 is 1, whereas 2, and 5 are 2.

Adding 1 to each and multiplying them together results in 36.

Therefore, the total number of factors of 700 is 36. Eighteen are positive, and eighteen factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The number factors cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 700 by Prime Factorization

The number 700 is a composite number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 700 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 700, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 700 can be expressed as:

700 = 2 x 2 x 5 x 5 x 7

Factors of 700 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.

For 700, the factor pairs can be found as:

1 x 700 = 700

2 x 350 = 700

4 x 175 = 700

5 x 140 = 700

7 x 100 = 700

10 x 70 = 700

14 x 50 = 700

20 x 35 = 700

25 x 28 = 700

The possible factor pairs of 700 are given as (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35), and (25, 28).

All these numbers in pairs, when multiplied, give 700 as the product.

The negative factor pairs of 700 are given as:

-1 x -700 = 700

-2 x -350 = 700

-4 x -175 = 700

-5 x -140 = 700

-7 x -100 = 700

-10 x -70 = 700

-14 x -50 = 700

-20 x -35 = 700

-25 x -28 = 700

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, –1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350, and -700 are called negative factors of 700.

The list of all the factors of 700, including positive as well as negative numbers, is given below.

Factor list of 700: 1, -1, 2, -2, 4, -4, 5, -5, 7, -7, 10, -10, 14, -14, 20, -20, 25, -25, 28, -28, 35, -35, 50, -50, 70, -70, 100, -100, 140, -140, 175, -175, 350, -350, 700, and -700

Factors of 700 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 700 are there?

Solution

The total number of Factors of 700 is 36.

Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.

Example 2

Find the factors of 700 using prime factorization.

Solution

The prime factorization of 700 is given as:

700 $\div$ 2 = 350 

350 $\div$ 2 = 175

175 $\div$ 5 = 35

35 $\div$ 5 = 7

7 $\div$ 7 = 1 

So the prime factorization of 700 can be written as:

2 x 2 x 5 x 5 x 7 = 700

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