1. Steps to find factors of 1944 using Division Method

Example: Find factors of 1944

  • Divide 1944 by 1: 1944 ÷ 1 : Remainder = 0
  • Divide 1944 by 2: 1944 ÷ 2 : Remainder = 0
  • Divide 1944 by 3: 1944 ÷ 3 : Remainder = 0
  • Divide 1944 by 4: 1944 ÷ 4 : Remainder = 0
  • Divide 1944 by 6: 1944 ÷ 6 : Remainder = 0
  • Divide 1944 by 8: 1944 ÷ 8 : Remainder = 0
  • Divide 1944 by 9: 1944 ÷ 9 : Remainder = 0
  • Divide 1944 by 12: 1944 ÷ 12 : Remainder = 0
  • Divide 1944 by 18: 1944 ÷ 18 : Remainder = 0
  • Divide 1944 by 24: 1944 ÷ 24 : Remainder = 0
  • Divide 1944 by 27: 1944 ÷ 27 : Remainder = 0
  • Divide 1944 by 36: 1944 ÷ 36 : Remainder = 0
  • Divide 1944 by 54: 1944 ÷ 54 : Remainder = 0
  • Divide 1944 by 72: 1944 ÷ 72 : Remainder = 0
  • Divide 1944 by 81: 1944 ÷ 81 : Remainder = 0
  • Divide 1944 by 108: 1944 ÷ 108 : Remainder = 0
  • Divide 1944 by 162: 1944 ÷ 162 : Remainder = 0
  • Divide 1944 by 216: 1944 ÷ 216 : Remainder = 0
  • Divide 1944 by 243: 1944 ÷ 243 : Remainder = 0
  • Divide 1944 by 324: 1944 ÷ 324 : Remainder = 0
  • Divide 1944 by 486: 1944 ÷ 486 : Remainder = 0
  • Divide 1944 by 648: 1944 ÷ 648 : Remainder = 0
  • Divide 1944 by 972: 1944 ÷ 972 : Remainder = 0
  • Divide 1944 by 1944: 1944 ÷ 1944 : Remainder = 0

Hence, Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, and 1944

2. Steps to find factors of 1944 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 1944 using the division method, follow these steps:

  • Step 1. Start dividing 1944 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 1944, which is 2. Divide 1944 by 2 to obtain the quotient (972).
    1944 ÷ 2 = 972
  • Step 3. Repeat step 1 with the obtained quotient (972).
    972 ÷ 2 = 486
    486 ÷ 2 = 243
    243 ÷ 3 = 81
    81 ÷ 3 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 1944 is, 1944 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1944 as shown below:

So, the prime factorization of 1944 is, 1944 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

3. Find factors of 1944 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 1944 would be the two numbers which, when multiplied, give 1944 as the result.

The following table represents the calculation of factors of 1944 in pairs:

Factor Pair Pair Factorization
1 and 1944 1 x 1944 = 1944
2 and 972 2 x 972 = 1944
3 and 648 3 x 648 = 1944
4 and 486 4 x 486 = 1944
6 and 324 6 x 324 = 1944
8 and 243 8 x 243 = 1944
9 and 216 9 x 216 = 1944
12 and 162 12 x 162 = 1944
18 and 108 18 x 108 = 1944
24 and 81 24 x 81 = 1944
27 and 72 27 x 72 = 1944
36 and 54 36 x 54 = 1944

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 1944. They are called negative pair factors.

Hence, the negative pairs of 1944 would be ( -1 , -1944 ) , ( -2 , -972 ) , ( -3 , -648 ) , ( -4 , -486 ) , ( -6 , -324 ) , ( -8 , -243 ) , ( -9 , -216 ) , ( -12 , -162 ) , ( -18 , -108 ) , ( -24 , -81 ) , ( -27 , -72 ) and ( -36 , -54 ) .

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

  • Each number is a factor of itself. Eg. 1944 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 1944.
  • Every number is a factor of zero (0), since 1944 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, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944 are exact divisors of 1944.
  • Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944. Each factor divides 1944 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944 are all less than or equal to 1944.

Frequently Asked Questions

  • Which is the smallest prime factor of 1944?

    Smallest prime factor of 1944 is 2.

  • Is 1944 a perfect square?

    No 1944 is not a perfect square.

  • What are five multiples of 1944?

    First five multiples of 1944 are 3888, 5832, 7776, 9720, 11664.

  • What is prime factorization of 1944?

    Prime factorization of 1944 is 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

  • What are factors of 1944?

    Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.

  • How do you find factors of a negative number? ( eg. -1944 )?

    Factors of -1944 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -243, -324, -486, -648, -972, -1944.

  • Is 1944 a whole number?

    Yes 1944 is a whole number.

  • Which is greatest factor of 1944?

    The greatest factor of 1944 is 972.

  • What are the prime factors of 1944?

    The factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
    Prime factors of 1944 are 2, 2, 2, 3, 3, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 1944. Can you help her?

Prime factors of 1944 are 2, 2, 2, 3, 3, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 1944?

Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
Even factors of 1944 are 2, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 648, 972, 1944.
Hence, product of even factors of 1944 is; 2 x 4 x 6 x 8 x 12 x 18 x 24 x 36 x 54 x 72 x 108 x 162 x 216 x 324 x 486 x 648 x 972 x 1944 = 2.030188233086892e+32.

Joy wants to calculate mean of all the factors of 1944. Help him in finding the mean of 1944.

Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1944 is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 81 + 108 + 162 + 216 + 243 + 324 + 486 + 648 + 972 + 1944 = 5460.
Hence, the mean of factors of 1944 is 5460 ÷ 24 = 227.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1944? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
Negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -27, -36, -54, -72, -81, -108, -162, -216, -243, -324, -486, -648, -972, -1944.

How many factors are there for 1944?

Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944.
So there are in total 24 factors.

Joey wants to write all the prime factors of 1944 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1944 are 2, 2, 2, 3, 3, 3, 3, 3.
So in exponential form it can be written as 23 x 35.

Kevin has been asked to write 23 factor(s) of 1944. Can you predict the answer?

23 factor(s) of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972.