# Factors of 650

Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, and 650

#### How to find factors of a number

 1.   Find factors of 650 using Division Method 2.   Find factors of 650 using Prime Factorization 3.   Find factors of 650 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 650

• Divide 650 by 1: 650 ÷ 1 : Remainder = 0
• Divide 650 by 2: 650 ÷ 2 : Remainder = 0
• Divide 650 by 5: 650 ÷ 5 : Remainder = 0
• Divide 650 by 10: 650 ÷ 10 : Remainder = 0
• Divide 650 by 13: 650 ÷ 13 : Remainder = 0
• Divide 650 by 25: 650 ÷ 25 : Remainder = 0
• Divide 650 by 26: 650 ÷ 26 : Remainder = 0
• Divide 650 by 50: 650 ÷ 50 : Remainder = 0
• Divide 650 by 65: 650 ÷ 65 : Remainder = 0
• Divide 650 by 130: 650 ÷ 130 : Remainder = 0
• Divide 650 by 325: 650 ÷ 325 : Remainder = 0
• Divide 650 by 650: 650 ÷ 650 : Remainder = 0

Hence, Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, and 650

#### 2. Steps to find factors of 650 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 650 using the division method, follow these steps:

• Step 1. Start dividing 650 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 650, which is 2. Divide 650 by 2 to obtain the quotient (325).
650 ÷ 2 = 325
• Step 3. Repeat step 1 with the obtained quotient (325).
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1

So, the prime factorization of 650 is, 650 = 2 x 5 x 5 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 650 as shown below:

So, the prime factorization of 650 is, 650 = 2 x 5 x 5 x 13.

#### 3. Find factors of 650 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 650 would be the two numbers which, when multiplied, give 650 as the result.

The following table represents the calculation of factors of 650 in pairs:

Factor Pair Pair Factorization
1 and 650 1 x 650 = 650
2 and 325 2 x 325 = 650
5 and 130 5 x 130 = 650
10 and 65 10 x 65 = 650
13 and 50 13 x 50 = 650
25 and 26 25 x 26 = 650

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 650. They are called negative pair factors.

Hence, the negative pairs of 650 would be ( -1 , -650 ) , ( -2 , -325 ) , ( -5 , -130 ) , ( -10 , -65 ) , ( -13 , -50 ) and ( -25 , -26 ) .

#### 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. 650 is a factor of itself.
• 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, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650 are exact divisors of 650.
• 1 is a factor of every number. Eg. 1 is a factor of 650.
• Every number is a factor of zero (0), since 650 x 0 = 0.

• What two numbers make 650?

Two numbers that make 650 are 2 and 325.

• What is prime factorization of 650?

Prime factorization of 650 is 2 x 5 x 5 x 13.

• Write some multiples of 650?

First five multiples of 650 are 1300, 1950, 2600, 3250.

• Which is the smallest prime factor of 650?

The smallest prime factor of 650 is 2.

• Is 650 a perfect square?

No 650 is not a perfect square.

• What is the sum of all factors of 650?

The sum of all factors of 650 is 1302.

• What are factors of 650?

Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.

• How do you find factors of a negative number? ( eg. -650 )?

Factors of -650 are -1, -2, -5, -10, -13, -25, -26, -50, -65, -130, -325, -650.

• Is 650 a whole number?

Yes 650 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 650. Help him in finding the mean of 650.

Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 650 is 1 + 2 + 5 + 10 + 13 + 25 + 26 + 50 + 65 + 130 + 325 + 650 = 1302.
Hence, the mean of factors of 650 is 1302 ÷ 12 = 108.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 650? Help her in writing all the factors.

Positive factors are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.
Negative factors are -1, -2, -5, -10, -13, -25, -26, -50, -65, -130, -325, -650.

Joey wants to write all the prime factors of 650 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 650 are 2, 5, 5, 13.
So in exponential form it can be written as 2 x 52 x 13.

Kevin has been asked to write 11 factor(s) of 650. Can you predict the answer?

11 factor(s) of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325.

Sammy is puzzled while calculating the prime factors of 650. Can you help him find them?

Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.
Prime factors of 650 are 2, 5, 5, 13

What is prime factorization of 650?

Prime factorization of 650 is 2 x 5 x 5 x 13 = 2 x 52 x 13.

Can you help Rubel to find out the product of the even factors of 650?

Factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650.
Even factors of 650 are 2, 10, 26, 50, 130, 650.
Hence, product of even factors of 650 is; 2 x 10 x 26 x 50 x 130 x 650 = 2197000000.