Factors of 9801 in pair are (1, 9801) , (3, 3267) , (9, 1089) , (11, 891) , (27, 363) , (33, 297) , (81, 121) and (99, 99)

How to find factors of a number in pair

Steps to find factors of 9801 in pair

Example: Find factors of 9801 in pair

Factor Pair Pair Factorization
1 and 9801 1 x 9801 = 9801
3 and 3267 3 x 3267 = 9801
9 and 1089 9 x 1089 = 9801
11 and 891 11 x 891 = 9801
27 and 363 27 x 363 = 9801
33 and 297 33 x 297 = 9801
81 and 121 81 x 121 = 9801
99 and 99 99 x 99 = 9801

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 9801. They are called negative pair factors.

Hence, the negative pairs of 9801 would be ( -1 , -9801 ) .

Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 9801 are 1 , 3 , 9 , 11 , 27 , 33 , 81 , 99 , 121 , 297 , 363 , 891 , 1089 , 3267 , 9801. So, factors of 9801 in pair are (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99).

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

  • Every factor of a number is an exact divisor of that number, example 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 are exact divisors of 9801.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 9801 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 9801.

Steps to find Factors of 9801

  • Step 1. Find all the numbers that would divide 9801 without leaving any remainder. Starting with the number 1 upto 4900 (half of 9801). The number 1 and the number itself are always factors of the given number.
    9801 ÷ 1 : Remainder = 0
    9801 ÷ 3 : Remainder = 0
    9801 ÷ 9 : Remainder = 0
    9801 ÷ 11 : Remainder = 0
    9801 ÷ 27 : Remainder = 0
    9801 ÷ 33 : Remainder = 0
    9801 ÷ 81 : Remainder = 0
    9801 ÷ 99 : Remainder = 0
    9801 ÷ 121 : Remainder = 0
    9801 ÷ 297 : Remainder = 0
    9801 ÷ 363 : Remainder = 0
    9801 ÷ 891 : Remainder = 0
    9801 ÷ 1089 : Remainder = 0
    9801 ÷ 3267 : Remainder = 0
    9801 ÷ 9801 : Remainder = 0

Hence, Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, and 9801

Frequently Asked Questions

  • Is 9801 a composite number?

    Yes 9801 is a composite number.

  • Is 9801 a perfect square?

    Yes 9801 is a perfect square.

  • Write all odd factors of 9801?

    The factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
    Odd factors of 9801 are 1 , 3 , 9 , 11 , 27 , 33 , 81 , 99 , 121 , 297 , 363 , 891 , 1089 , 3267 , 9801.

  • What is the mean of all prime factors of 9801?

    Factors of 9801 are 1 , 3 , 9 , 11 , 27 , 33 , 81 , 99 , 121 , 297 , 363 , 891 , 1089 , 3267 , 9801. Prime factors of 9801 are 3 , 3 , 3 , 3 , 11 , 11. Therefore mean of prime factors of 9801 is (3 + 3 + 3 + 3 + 11 + 11) / 6 = 5.67.

  • What do you mean by proper divisors?

    A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

Examples of Factors

Can you help Rubel in arranging 9801 blocks in order to form a rectangle in all possible ways? For arranging 9801 blocks in order to form a rectangle in all possible ways we need to find factors of 9801 in pair.

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801. So, factors of 9801 in pair are (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99).

How many total number of factors of 9801 in pair are possible?

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801. Hence, the factors of 9801 in pair are (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99). Therefore, in total 8 pairs of factors are possible.

Sammy wants to write all the negative factors of 9801 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 9801 are -1, -3, -9, -11, -27, -33, -81, -99, -121, -297, -363, -891, -1089, -3267, -9801. Hence, factors of 9801 in pair are (-1,-9801), (-3,-3267), (-9,-1089), (-11,-891), (-27,-363), (-33,-297), (-81,-121), (-99,-99).

Find the product of all prime factors of 9801.

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801. Prime factors are 3, 3, 3, 3, 11, 11. So, the product of all prime factors of 9801 would be 3 x 3 x 3 x 3 x 11 x 11 = 9801.

A student has been assigned the following tasks by the teacher:
- Finding out all positive factors of 9801.
- Writing all prime factors of 9801.
- Writing all the possible factors of 9801 in pair.
Help him in writing all these.

Positive factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Prime factors of 9801 are 3, 3, 3, 3, 11, 11.
Factors of 9801 in pair are (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99).

Can you help Sammy list the factors of 9801 and also find the factor pairs?

Factors of 9801 are 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801.
Factors of 9801 in pair are (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99).

Help Diji in finding factors of 9801 by Prime Factorization method and then sorting factors of 9801 in pairs.

Prime factorization of 9801 is 3 x 3 x 3 x 3 x 11 x 11. Factors of 9801 in pair can be written as (1,9801), (3,3267), (9,1089), (11,891), (27,363), (33,297), (81,121), (99,99).

Write the smallest prime factor of 9801.

Smallest prime factor of 9801 is 3.