# Factors of 3500

Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, and 3500

#### How to find factors of a number

 1.   Find factors of 3500 using Division Method 2.   Find factors of 3500 using Prime Factorization 3.   Find factors of 3500 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 3500

• Divide 3500 by 1: 3500 ÷ 1 : Remainder = 0
• Divide 3500 by 2: 3500 ÷ 2 : Remainder = 0
• Divide 3500 by 4: 3500 ÷ 4 : Remainder = 0
• Divide 3500 by 5: 3500 ÷ 5 : Remainder = 0
• Divide 3500 by 7: 3500 ÷ 7 : Remainder = 0
• Divide 3500 by 10: 3500 ÷ 10 : Remainder = 0
• Divide 3500 by 14: 3500 ÷ 14 : Remainder = 0
• Divide 3500 by 20: 3500 ÷ 20 : Remainder = 0
• Divide 3500 by 25: 3500 ÷ 25 : Remainder = 0
• Divide 3500 by 28: 3500 ÷ 28 : Remainder = 0
• Divide 3500 by 35: 3500 ÷ 35 : Remainder = 0
• Divide 3500 by 50: 3500 ÷ 50 : Remainder = 0
• Divide 3500 by 70: 3500 ÷ 70 : Remainder = 0
• Divide 3500 by 100: 3500 ÷ 100 : Remainder = 0
• Divide 3500 by 125: 3500 ÷ 125 : Remainder = 0
• Divide 3500 by 140: 3500 ÷ 140 : Remainder = 0
• Divide 3500 by 175: 3500 ÷ 175 : Remainder = 0
• Divide 3500 by 250: 3500 ÷ 250 : Remainder = 0
• Divide 3500 by 350: 3500 ÷ 350 : Remainder = 0
• Divide 3500 by 500: 3500 ÷ 500 : Remainder = 0
• Divide 3500 by 700: 3500 ÷ 700 : Remainder = 0
• Divide 3500 by 875: 3500 ÷ 875 : Remainder = 0
• Divide 3500 by 1750: 3500 ÷ 1750 : Remainder = 0
• Divide 3500 by 3500: 3500 ÷ 3500 : Remainder = 0

Hence, Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, and 3500

#### 2. Steps to find factors of 3500 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 3500 using the division method, follow these steps:

• Step 1. Start dividing 3500 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 3500, which is 2. Divide 3500 by 2 to obtain the quotient (1750).
3500 ÷ 2 = 1750
• Step 3. Repeat step 1 with the obtained quotient (1750).
1750 ÷ 2 = 875
875 ÷ 5 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 3500 is, 3500 = 2 x 2 x 5 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3500 as shown below:

So, the prime factorization of 3500 is, 3500 = 2 x 2 x 5 x 5 x 5 x 7.

#### 3. Find factors of 3500 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 3500 would be the two numbers which, when multiplied, give 3500 as the result.

The following table represents the calculation of factors of 3500 in pairs:

Factor Pair Pair Factorization
1 and 3500 1 x 3500 = 3500
2 and 1750 2 x 1750 = 3500
4 and 875 4 x 875 = 3500
5 and 700 5 x 700 = 3500
7 and 500 7 x 500 = 3500
10 and 350 10 x 350 = 3500
14 and 250 14 x 250 = 3500
20 and 175 20 x 175 = 3500
25 and 140 25 x 140 = 3500
28 and 125 28 x 125 = 3500
35 and 100 35 x 100 = 3500
50 and 70 50 x 70 = 3500

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 3500. They are called negative pair factors.

Hence, the negative pairs of 3500 would be ( -1 , -3500 ) , ( -2 , -1750 ) , ( -4 , -875 ) , ( -5 , -700 ) , ( -7 , -500 ) , ( -10 , -350 ) , ( -14 , -250 ) , ( -20 , -175 ) , ( -25 , -140 ) , ( -28 , -125 ) , ( -35 , -100 ) and ( -50 , -70 ) .

#### 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. 3500 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 3500.
• Every number is a factor of zero (0), since 3500 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, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 are exact divisors of 3500.
• Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500. Each factor divides 3500 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, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500 are all less than or equal to 3500.

• What is prime factorization of 3500?

Prime factorization of 3500 is 2 x 2 x 5 x 5 x 5 x 7.

• How do you find factors of a negative number? ( eg. -3500 )?

Factors of -3500 are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -125, -140, -175, -250, -350, -500, -700, -875, -1750, -3500.

• What are the prime factors of 3500?

The factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
Prime factors of 3500 are 2, 2, 5, 5, 5, 7.

• What are pair factors of 3500?

The pair factors of 3500 are (1,3500), (2,1750), (4,875), (5,700), (7,500), (10,350), (14,250), (20,175), (25,140), (28,125), (35,100), (50,70).

• What is the greatest prime factors of 3500?

The greatest prime factor of 3500 is 7.

• What are six multiples of 3500?

First five multiples of 3500 are 7000, 10500, 14000, 17500, 21000, 24500.

• What are factors of 3500?

Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.

• Which is the smallest prime factor of 3500?

Smallest prime factor of 3500 is 2.

• Is 3500 a whole number?

Yes 3500 is a whole number.

#### Examples of Factors

Kevin has been asked to write 23 factor(s) of 3500. Can you predict the answer?

23 factor(s) of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750.

Sammy is puzzled while calculating the prime factors of 3500. Can you help him find them?

Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
Prime factors of 3500 are 2, 2, 5, 5, 5, 7

What is prime factorization of 3500?

Prime factorization of 3500 is 2 x 2 x 5 x 5 x 5 x 7 = 22 x 53 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 3500. Can you help her?

Prime factors of 3500 are 2, 2, 5, 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 3500?

Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
Even factors of 3500 are 2, 4, 10, 14, 20, 28, 50, 70, 100, 140, 250, 350, 500, 700, 1750, 3500.
Hence, product of even factors of 3500 is; 2 x 4 x 10 x 14 x 20 x 28 x 50 x 70 x 100 x 140 x 250 x 350 x 500 x 700 x 1750 x 3500 = 5.764801e+30.

Joy wants to calculate mean of all the factors of 3500. Help him in finding the mean of 3500.

Factors of 3500 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3500 is 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 125 + 140 + 175 + 250 + 350 + 500 + 700 + 875 + 1750 + 3500 = 8736.
Hence, the mean of factors of 3500 is 8736 ÷ 24 = 364.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3500? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 125, 140, 175, 250, 350, 500, 700, 875, 1750, 3500.
Negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -125, -140, -175, -250, -350, -500, -700, -875, -1750, -3500.