# Factors of 700

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

#### How to find factors of a number

 1.   Find factors of 700 using Division Method 2.   Find factors of 700 using Prime Factorization 3.   Find factors of 700 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 700

• Divide 700 by 1: 700 ÷ 1 : Remainder = 0
• Divide 700 by 2: 700 ÷ 2 : Remainder = 0
• Divide 700 by 4: 700 ÷ 4 : Remainder = 0
• Divide 700 by 5: 700 ÷ 5 : Remainder = 0
• Divide 700 by 7: 700 ÷ 7 : Remainder = 0
• Divide 700 by 10: 700 ÷ 10 : Remainder = 0
• Divide 700 by 14: 700 ÷ 14 : Remainder = 0
• Divide 700 by 20: 700 ÷ 20 : Remainder = 0
• Divide 700 by 25: 700 ÷ 25 : Remainder = 0
• Divide 700 by 28: 700 ÷ 28 : Remainder = 0
• Divide 700 by 35: 700 ÷ 35 : Remainder = 0
• Divide 700 by 50: 700 ÷ 50 : Remainder = 0
• Divide 700 by 70: 700 ÷ 70 : Remainder = 0
• Divide 700 by 100: 700 ÷ 100 : Remainder = 0
• Divide 700 by 140: 700 ÷ 140 : Remainder = 0
• Divide 700 by 175: 700 ÷ 175 : Remainder = 0
• Divide 700 by 350: 700 ÷ 350 : Remainder = 0
• Divide 700 by 700: 700 ÷ 700 : Remainder = 0

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

#### 2. Steps to find factors of 700 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 700 using the division method, follow these steps:

• Step 1. Start dividing 700 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 700, which is 2. Divide 700 by 2 to obtain the quotient (350).
700 ÷ 2 = 350
• Step 3. Repeat step 1 with the obtained quotient (350).
350 ÷ 2 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 700 is, 700 = 2 x 2 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 700 as shown below:

So, the prime factorization of 700 is, 700 = 2 x 2 x 5 x 5 x 7.

#### 3. Find factors of 700 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 700 would be the two numbers which, when multiplied, give 700 as the result.

The following table represents the calculation of factors of 700 in pairs:

Factor Pair Pair Factorization
1 and 700 1 x 700 = 700
2 and 350 2 x 350 = 700
4 and 175 4 x 175 = 700
5 and 140 5 x 140 = 700
7 and 100 7 x 100 = 700
10 and 70 10 x 70 = 700
14 and 50 14 x 50 = 700
20 and 35 20 x 35 = 700
25 and 28 25 x 28 = 700

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 700. They are called negative pair factors.

Hence, the negative pairs of 700 would be ( -1 , -700 ) , ( -2 , -350 ) , ( -4 , -175 ) , ( -5 , -140 ) , ( -7 , -100 ) , ( -10 , -70 ) , ( -14 , -50 ) , ( -20 , -35 ) and ( -25 , -28 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 700 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 700.
• Every number is a factor of zero (0), since 700 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 are exact divisors of 700.
• Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700. Each factor divides 700 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700 are all less than or equal to 700.

• Which is the smallest prime factor of 700?

The smallest prime factor of 700 is 2.

• Is 700 a whole number?

Yes 700 is a whole number.

• What are the prime 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.
Prime factors of 700 are 2, 2, 5, 5, 7.

• What two numbers make 700?

Two numbers that make 700 are 2 and 350.

• What are multiples of 700?

First five multiples of 700 are 1400, 2100, 2800, 3500.

• What is the sum of all factors of 700?

The sum of all factors of 700 is 1736.

• What are five multiples of 700?

First five multiples of 700 are 1400, 2100, 2800, 3500, 4200.

• Is 700 a perfect square?

No 700 is not a perfect square.

• What is the greatest prime factors of 700?

The greatest prime factor of 700 is 7.

#### Examples of Factors

How many factors are there for 700?

Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.
So there are in total 18 factors.

Kevin has been asked to write 17 factor(s) of 700. Can you predict the answer?

17 factor(s) of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350.

Sammy is puzzled while calculating the prime factors of 700. Can you help him find them?

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

What is prime factorization of 700?

Prime factorization of 700 is 2 x 2 x 5 x 5 x 7 = 22 x 52 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 700. Can you help her?

Prime factors of 700 are 2, 2, 5, 5, 7.
Hence, the product of prime factors of 70.

Can you help Rubel to find out the product of the even factors of 700?

Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.
Even factors of 700 are 2, 4, 10, 14, 20, 28, 50, 70, 100, 140, 350, 700.
Hence, product of even factors of 700 is; 2 x 4 x 10 x 14 x 20 x 28 x 50 x 70 x 100 x 140 x 350 x 700 = 7529536000000000000.

Joy wants to calculate mean of all the factors of 700. Help him in finding the mean of 700.

Factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 700 is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 140 + 175 + 350 + 700 = 1736.
Hence, the mean of factors of 700 is 1736 ÷ 18 = 96.44.