# Factors of 680

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680

#### How to find factors of a number

 1.   Find factors of 680 using Division Method 2.   Find factors of 680 using Prime Factorization 3.   Find factors of 680 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 680

• Divide 680 by 1: 680 ÷ 1 : Remainder = 0
• Divide 680 by 2: 680 ÷ 2 : Remainder = 0
• Divide 680 by 4: 680 ÷ 4 : Remainder = 0
• Divide 680 by 5: 680 ÷ 5 : Remainder = 0
• Divide 680 by 8: 680 ÷ 8 : Remainder = 0
• Divide 680 by 10: 680 ÷ 10 : Remainder = 0
• Divide 680 by 17: 680 ÷ 17 : Remainder = 0
• Divide 680 by 20: 680 ÷ 20 : Remainder = 0
• Divide 680 by 34: 680 ÷ 34 : Remainder = 0
• Divide 680 by 40: 680 ÷ 40 : Remainder = 0
• Divide 680 by 68: 680 ÷ 68 : Remainder = 0
• Divide 680 by 85: 680 ÷ 85 : Remainder = 0
• Divide 680 by 136: 680 ÷ 136 : Remainder = 0
• Divide 680 by 170: 680 ÷ 170 : Remainder = 0
• Divide 680 by 340: 680 ÷ 340 : Remainder = 0
• Divide 680 by 680: 680 ÷ 680 : Remainder = 0

Hence, Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, and 680

#### 2. Steps to find factors of 680 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 680 using the division method, follow these steps:

• Step 1. Start dividing 680 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 680, which is 2. Divide 680 by 2 to obtain the quotient (340).
680 ÷ 2 = 340
• Step 3. Repeat step 1 with the obtained quotient (340).
340 ÷ 2 = 170
170 ÷ 2 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1

So, the prime factorization of 680 is, 680 = 2 x 2 x 2 x 5 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 680 as shown below:

So, the prime factorization of 680 is, 680 = 2 x 2 x 2 x 5 x 17.

#### 3. Find factors of 680 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 680 would be the two numbers which, when multiplied, give 680 as the result.

The following table represents the calculation of factors of 680 in pairs:

Factor Pair Pair Factorization
1 and 680 1 x 680 = 680
2 and 340 2 x 340 = 680
4 and 170 4 x 170 = 680
5 and 136 5 x 136 = 680
8 and 85 8 x 85 = 680
10 and 68 10 x 68 = 680
17 and 40 17 x 40 = 680
20 and 34 20 x 34 = 680

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 680. They are called negative pair factors.

Hence, the negative pairs of 680 would be ( -1 , -680 ) , ( -2 , -340 ) , ( -4 , -170 ) , ( -5 , -136 ) , ( -8 , -85 ) , ( -10 , -68 ) , ( -17 , -40 ) and ( -20 , -34 ) .

#### 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. 680 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 680.
• Every number is a factor of zero (0), since 680 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, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 are exact divisors of 680.
• Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680. Each factor divides 680 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680 are all less than or equal to 680.

• What are the pair factors of 680?

Pair factors of 680 are (1,680), (2,340), (4,170), (5,136), (8,85), (10,68), (17,40), (20,34).

• What are five multiples of 680?

First five multiples of 680 are 1360, 2040, 2720, 3400, 4080.

• What two numbers make 680?

Two numbers that make 680 are 2 and 340.

• What is the sum of all factors of 680?

The sum of all factors of 680 is 1620.

• What are factors of -680?

Factors of -680 are -1, -2, -4, -5, -8, -10, -17, -20, -34, -40, -68, -85, -136, -170, -340, -680.

• What are factors of 680?

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.

• Is 680 a perfect square?

No 680 is not a perfect square.

• Which is the smallest prime factor of 680?

Smallest prime factor of 680 is 2.

• Which is greatest factor of 680?

The greatest factor of 680 is 340.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 680?

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Odd factors of 680 are 1, 5, 17, 85.
Hence product of odd factors of 680 is; 1 x 5 x 17 x 85 = 7225.

Joey wants to write all the prime factors of 680 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 680 are 2, 2, 2, 5, 17.
So in exponential form it can be written as 23 x 5 x 17.

How many factors are there for 680?

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 680. Can you predict the answer?

15 factor(s) of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340.

Sammy is puzzled while calculating the prime factors of 680. Can you help him find them?

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Prime factors of 680 are 2, 2, 2, 5, 17

What is prime factorization of 680?

Prime factorization of 680 is 2 x 2 x 2 x 5 x 17 = 23 x 5 x 17.

Can you help Rubel to find out the product of the even factors of 680?

Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.
Even factors of 680 are 2, 4, 8, 10, 20, 34, 40, 68, 136, 170, 340, 680.
Hence, product of even factors of 680 is; 2 x 4 x 8 x 10 x 20 x 34 x 40 x 68 x 136 x 170 x 340 x 680 = 6327518887936000000.