1. Steps to find factors of 689 using Division Method

Example: Find factors of 689

  • Divide 689 by 1: 689 ÷ 1 : Remainder = 0
  • Divide 689 by 13: 689 ÷ 13 : Remainder = 0
  • Divide 689 by 53: 689 ÷ 53 : Remainder = 0
  • Divide 689 by 689: 689 ÷ 689 : Remainder = 0

Hence, Factors of 689 are 1, 13, 53, and 689

2. Steps to find factors of 689 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 689 using the division method, follow these steps:

  • Step 1. Start dividing 689 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 689, which is 13. Divide 689 by 13 to obtain the quotient (53).
    689 ÷ 13 = 53
  • Step 3. Repeat step 1 with the obtained quotient (53).
    53 ÷ 53 = 1

So, the prime factorization of 689 is, 689 = 13 x 53.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 689 as shown below:

So, the prime factorization of 689 is, 689 = 13 x 53.

3. Find factors of 689 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 689 would be the two numbers which, when multiplied, give 689 as the result.

The following table represents the calculation of factors of 689 in pairs:

Factor Pair Pair Factorization
1 and 689 1 x 689 = 689
13 and 53 13 x 53 = 689

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 689. They are called negative pair factors.

Hence, the negative pairs of 689 would be ( -1 , -689 ) , ( -13 , -53 ) .

How can we define factors?

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

Properties of factors

  • Every factor of a number is an exact divisor of that number, example 1, 13, 53, 689 are exact divisors of 689.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 689 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 689.

Frequently Asked Questions

  • What are the pair factors of 689?

    Pair factors of 689 are (1,689), (13,53).

  • What are five multiples of 689?

    First five multiples of 689 are 1378, 2067, 2756, 3445, 4134.

  • What two numbers make 689?

    Two numbers that make 689 are 13 and 53.

  • What is the sum of all factors of 689?

    The sum of all factors of 689 is 756.

  • What are factors of -689?

    Factors of -689 are -1, -13, -53, -689.

  • What are factors of 689?

    Factors of 689 are 1, 13, 53, 689.

  • Is 689 a perfect square?

    No 689 is not a perfect square.

  • Which is the smallest prime factor of 689?

    Smallest prime factor of 689 is 13.

  • Which is greatest factor of 689?

    The greatest factor of 689 is 53.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 689?

Factors of 689 are 1, 13, 53, 689.
Odd factors of 689 are 1, 13, 53, 689.
Hence product of odd factors of 689 is; 1 x 13 x 53 x 689 = 474721.

Joey wants to write all the prime factors of 689 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 689 are 13, 53.
So in exponential form it can be written as 13 x 53.

How many factors are there for 689?

Factors of 689 are 1, 13, 53, 689.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 689. Can you predict the answer?

3 factor(s) of 689 are 1, 13, 53.

Sammy is puzzled while calculating the prime factors of 689. Can you help him find them?

Factors of 689 are 1, 13, 53, 689.
Prime factors of 689 are 13, 53

What is prime factorization of 689?

Prime factorization of 689 is 13 x 53 = 13 x 53.

Can you help Rubel to find out the product of the even factors of 689?

Factors of 689 are 1, 13, 53, 689.
Even factors of 689 are 0.
Hence, product of even factors of 689 is; 0 = 0.