1. Steps to find factors of 986 using Division Method

Example: Find factors of 986

  • Divide 986 by 1: 986 ÷ 1 : Remainder = 0
  • Divide 986 by 2: 986 ÷ 2 : Remainder = 0
  • Divide 986 by 17: 986 ÷ 17 : Remainder = 0
  • Divide 986 by 29: 986 ÷ 29 : Remainder = 0
  • Divide 986 by 34: 986 ÷ 34 : Remainder = 0
  • Divide 986 by 58: 986 ÷ 58 : Remainder = 0
  • Divide 986 by 493: 986 ÷ 493 : Remainder = 0
  • Divide 986 by 986: 986 ÷ 986 : Remainder = 0

Hence, Factors of 986 are 1, 2, 17, 29, 34, 58, 493, and 986

2. Steps to find factors of 986 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 986 using the division method, follow these steps:

  • Step 1. Start dividing 986 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 986, which is 2. Divide 986 by 2 to obtain the quotient (493).
    986 ÷ 2 = 493
  • Step 3. Repeat step 1 with the obtained quotient (493).
    493 ÷ 17 = 29
    29 ÷ 29 = 1

So, the prime factorization of 986 is, 986 = 2 x 17 x 29.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 986 as shown below:

So, the prime factorization of 986 is, 986 = 2 x 17 x 29.

3. Find factors of 986 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 986 would be the two numbers which, when multiplied, give 986 as the result.

The following table represents the calculation of factors of 986 in pairs:

Factor Pair Pair Factorization
1 and 986 1 x 986 = 986
2 and 493 2 x 493 = 986
17 and 58 17 x 58 = 986
29 and 34 29 x 34 = 986

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 986. They are called negative pair factors.

Hence, the negative pairs of 986 would be ( -1 , -986 ) , ( -2 , -493 ) , ( -17 , -58 ) and ( -29 , -34 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 986 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, 17, 29, 34, 58, 493, 986 are exact divisors of 986.
  • 1 is a factor of every number. Eg. 1 is a factor of 986.
  • Every number is a factor of zero (0), since 986 x 0 = 0.

Frequently Asked Questions

  • What are the pair factors of 986?

    Pair factors of 986 are (1,986), (2,493), (17,58), (29,34).

  • What are five multiples of 986?

    First five multiples of 986 are 1972, 2958, 3944, 4930, 5916.

  • What two numbers make 986?

    Two numbers that make 986 are 2 and 493.

  • What is the sum of all factors of 986?

    The sum of all factors of 986 is 1620.

  • What are factors of -986?

    Factors of -986 are -1, -2, -17, -29, -34, -58, -493, -986.

  • What are factors of 986?

    Factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986.

  • Is 986 a perfect square?

    No 986 is not a perfect square.

  • Which is the smallest prime factor of 986?

    Smallest prime factor of 986 is 2.

  • Which is greatest factor of 986?

    The greatest factor of 986 is 493.

Examples of Factors

Can you help Sammy find out the product of the odd factors of 986?

Factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986.
Odd factors of 986 are 1, 17, 29, 493.
Hence product of odd factors of 986 is; 1 x 17 x 29 x 493 = 243049.

Joey wants to write all the prime factors of 986 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 986 are 2, 17, 29.
So in exponential form it can be written as 2 x 17 x 29.

How many factors are there for 986?

Factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 986. Can you predict the answer?

7 factor(s) of 986 are 1, 2, 17, 29, 34, 58, 493.

Sammy is puzzled while calculating the prime factors of 986. Can you help him find them?

Factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986.
Prime factors of 986 are 2, 17, 29

What is prime factorization of 986?

Prime factorization of 986 is 2 x 17 x 29 = 2 x 17 x 29.

Can you help Rubel to find out the product of the even factors of 986?

Factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986.
Even factors of 986 are 2, 34, 58, 986.
Hence, product of even factors of 986 is; 2 x 34 x 58 x 986 = 3888784.