Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, and 1980

How to find factors of a number

1. Steps to find factors of 1980 using Division Method

Example: Find factors of 1980

  • Divide 1980 by 1: 1980 ÷ 1 : Remainder = 0
  • Divide 1980 by 2: 1980 ÷ 2 : Remainder = 0
  • Divide 1980 by 3: 1980 ÷ 3 : Remainder = 0
  • Divide 1980 by 4: 1980 ÷ 4 : Remainder = 0
  • Divide 1980 by 5: 1980 ÷ 5 : Remainder = 0
  • Divide 1980 by 6: 1980 ÷ 6 : Remainder = 0
  • Divide 1980 by 9: 1980 ÷ 9 : Remainder = 0
  • Divide 1980 by 10: 1980 ÷ 10 : Remainder = 0
  • Divide 1980 by 11: 1980 ÷ 11 : Remainder = 0
  • Divide 1980 by 12: 1980 ÷ 12 : Remainder = 0
  • Divide 1980 by 15: 1980 ÷ 15 : Remainder = 0
  • Divide 1980 by 18: 1980 ÷ 18 : Remainder = 0
  • Divide 1980 by 20: 1980 ÷ 20 : Remainder = 0
  • Divide 1980 by 22: 1980 ÷ 22 : Remainder = 0
  • Divide 1980 by 30: 1980 ÷ 30 : Remainder = 0
  • Divide 1980 by 33: 1980 ÷ 33 : Remainder = 0
  • Divide 1980 by 36: 1980 ÷ 36 : Remainder = 0
  • Divide 1980 by 44: 1980 ÷ 44 : Remainder = 0
  • Divide 1980 by 45: 1980 ÷ 45 : Remainder = 0
  • Divide 1980 by 55: 1980 ÷ 55 : Remainder = 0
  • Divide 1980 by 60: 1980 ÷ 60 : Remainder = 0
  • Divide 1980 by 66: 1980 ÷ 66 : Remainder = 0
  • Divide 1980 by 90: 1980 ÷ 90 : Remainder = 0
  • Divide 1980 by 99: 1980 ÷ 99 : Remainder = 0
  • Divide 1980 by 110: 1980 ÷ 110 : Remainder = 0
  • Divide 1980 by 132: 1980 ÷ 132 : Remainder = 0
  • Divide 1980 by 165: 1980 ÷ 165 : Remainder = 0
  • Divide 1980 by 180: 1980 ÷ 180 : Remainder = 0
  • Divide 1980 by 198: 1980 ÷ 198 : Remainder = 0
  • Divide 1980 by 220: 1980 ÷ 220 : Remainder = 0
  • Divide 1980 by 330: 1980 ÷ 330 : Remainder = 0
  • Divide 1980 by 396: 1980 ÷ 396 : Remainder = 0
  • Divide 1980 by 495: 1980 ÷ 495 : Remainder = 0
  • Divide 1980 by 660: 1980 ÷ 660 : Remainder = 0
  • Divide 1980 by 990: 1980 ÷ 990 : Remainder = 0
  • Divide 1980 by 1980: 1980 ÷ 1980 : Remainder = 0

Hence, Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, and 1980

2. Steps to find factors of 1980 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 1980 using the division method, follow these steps:

  • Step 1. Start dividing 1980 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 1980, which is 2. Divide 1980 by 2 to obtain the quotient (990).
    1980 ÷ 2 = 990
  • Step 3. Repeat step 1 with the obtained quotient (990).
    990 ÷ 2 = 495
    495 ÷ 3 = 165
    165 ÷ 3 = 55
    55 ÷ 5 = 11
    11 ÷ 11 = 1

So, the prime factorization of 1980 is, 1980 = 2 x 2 x 3 x 3 x 5 x 11.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1980 as shown below:

So, the prime factorization of 1980 is, 1980 = 2 x 2 x 3 x 3 x 5 x 11.

3. Find factors of 1980 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 1980 would be the two numbers which, when multiplied, give 1980 as the result.

The following table represents the calculation of factors of 1980 in pairs:

Factor Pair Pair Factorization
1 and 1980 1 x 1980 = 1980
2 and 990 2 x 990 = 1980
3 and 660 3 x 660 = 1980
4 and 495 4 x 495 = 1980
5 and 396 5 x 396 = 1980
6 and 330 6 x 330 = 1980
9 and 220 9 x 220 = 1980
10 and 198 10 x 198 = 1980
11 and 180 11 x 180 = 1980
12 and 165 12 x 165 = 1980
15 and 132 15 x 132 = 1980
18 and 110 18 x 110 = 1980
20 and 99 20 x 99 = 1980
22 and 90 22 x 90 = 1980
30 and 66 30 x 66 = 1980
33 and 60 33 x 60 = 1980
36 and 55 36 x 55 = 1980
44 and 45 44 x 45 = 1980

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 1980. They are called negative pair factors.

Hence, the negative pairs of 1980 would be ( -1 , -1980 ) , ( -2 , -990 ) , ( -3 , -660 ) , ( -4 , -495 ) , ( -5 , -396 ) , ( -6 , -330 ) , ( -9 , -220 ) , ( -10 , -198 ) , ( -11 , -180 ) , ( -12 , -165 ) , ( -15 , -132 ) , ( -18 , -110 ) , ( -20 , -99 ) , ( -22 , -90 ) , ( -30 , -66 ) , ( -33 , -60 ) , ( -36 , -55 ) and ( -44 , -45 ) .

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. 1980 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1980.
  • Every number is a factor of zero (0), since 1980 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, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 are exact divisors of 1980.
  • Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980. Each factor divides 1980 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 are all less than or equal to 1980.

Frequently Asked Questions

  • Which is the smallest prime factor of 1980?

    Smallest prime factor of 1980 is 2.

  • Is 1980 a perfect square?

    No 1980 is not a perfect square.

  • What are five multiples of 1980?

    First five multiples of 1980 are 3960, 5940, 7920, 9900, 11880.

  • What is prime factorization of 1980?

    Prime factorization of 1980 is 2 x 2 x 3 x 3 x 5 x 11.

  • What are factors of 1980?

    Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.

  • How do you find factors of a negative number? ( eg. -1980 )?

    Factors of -1980 are -1, -2, -3, -4, -5, -6, -9, -10, -11, -12, -15, -18, -20, -22, -30, -33, -36, -44, -45, -55, -60, -66, -90, -99, -110, -132, -165, -180, -198, -220, -330, -396, -495, -660, -990, -1980.

  • Is 1980 a whole number?

    Yes 1980 is a whole number.

  • Which is greatest factor of 1980?

    The greatest factor of 1980 is 990.

  • What are the prime factors of 1980?

    The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
    Prime factors of 1980 are 2, 2, 3, 3, 5, 11.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1980. Can you help her?

Prime factors of 1980 are 2, 2, 3, 3, 5, 11.
Hence, the product of prime factors of 330.

Can you help Rubel to find out the product of the even factors of 1980?

Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
Even factors of 1980 are 2, 4, 6, 10, 12, 18, 20, 22, 30, 36, 44, 60, 66, 90, 110, 132, 180, 198, 220, 330, 396, 660, 990, 1980.
Hence, product of even factors of 1980 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 22 x 30 x 36 x 44 x 60 x 66 x 90 x 110 x 132 x 180 x 198 x 220 x 330 x 396 x 660 x 990 x 1980 = 1.487107045191379e+43.

Joy wants to calculate mean of all the factors of 1980. Help him in finding the mean of 1980.

Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1980 is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 11 + 12 + 15 + 18 + 20 + 22 + 30 + 33 + 36 + 44 + 45 + 55 + 60 + 66 + 90 + 99 + 110 + 132 + 165 + 180 + 198 + 220 + 330 + 396 + 495 + 660 + 990 + 1980 = 6552.
Hence, the mean of factors of 1980 is 6552 ÷ 36 = 182.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1980? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
Negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -11, -12, -15, -18, -20, -22, -30, -33, -36, -44, -45, -55, -60, -66, -90, -99, -110, -132, -165, -180, -198, -220, -330, -396, -495, -660, -990, -1980.

How many factors are there for 1980?

Factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980.
So there are in total 36 factors.

Joey wants to write all the prime factors of 1980 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1980 are 2, 2, 3, 3, 5, 11.
So in exponential form it can be written as 22 x 32 x 5 x 11.

Kevin has been asked to write 35 factor(s) of 1980. Can you predict the answer?

35 factor(s) of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990.