1. Steps to find factors of 3584 using Division Method

Example: Find factors of 3584

  • Divide 3584 by 1: 3584 ÷ 1 : Remainder = 0
  • Divide 3584 by 2: 3584 ÷ 2 : Remainder = 0
  • Divide 3584 by 4: 3584 ÷ 4 : Remainder = 0
  • Divide 3584 by 7: 3584 ÷ 7 : Remainder = 0
  • Divide 3584 by 8: 3584 ÷ 8 : Remainder = 0
  • Divide 3584 by 14: 3584 ÷ 14 : Remainder = 0
  • Divide 3584 by 16: 3584 ÷ 16 : Remainder = 0
  • Divide 3584 by 28: 3584 ÷ 28 : Remainder = 0
  • Divide 3584 by 32: 3584 ÷ 32 : Remainder = 0
  • Divide 3584 by 56: 3584 ÷ 56 : Remainder = 0
  • Divide 3584 by 64: 3584 ÷ 64 : Remainder = 0
  • Divide 3584 by 112: 3584 ÷ 112 : Remainder = 0
  • Divide 3584 by 128: 3584 ÷ 128 : Remainder = 0
  • Divide 3584 by 224: 3584 ÷ 224 : Remainder = 0
  • Divide 3584 by 256: 3584 ÷ 256 : Remainder = 0
  • Divide 3584 by 448: 3584 ÷ 448 : Remainder = 0
  • Divide 3584 by 512: 3584 ÷ 512 : Remainder = 0
  • Divide 3584 by 896: 3584 ÷ 896 : Remainder = 0
  • Divide 3584 by 1792: 3584 ÷ 1792 : Remainder = 0
  • Divide 3584 by 3584: 3584 ÷ 3584 : Remainder = 0

Hence, Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, and 3584

2. Steps to find factors of 3584 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 3584 using the division method, follow these steps:

  • Step 1. Start dividing 3584 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 3584, which is 2. Divide 3584 by 2 to obtain the quotient (1792).
    3584 ÷ 2 = 1792
  • Step 3. Repeat step 1 with the obtained quotient (1792).
    1792 ÷ 2 = 896
    896 ÷ 2 = 448
    448 ÷ 2 = 224
    224 ÷ 2 = 112
    112 ÷ 2 = 56
    56 ÷ 2 = 28
    28 ÷ 2 = 14
    14 ÷ 2 = 7
    7 ÷ 7 = 1

So, the prime factorization of 3584 is, 3584 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 3584 as shown below:

So, the prime factorization of 3584 is, 3584 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

3. Find factors of 3584 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 3584 would be the two numbers which, when multiplied, give 3584 as the result.

The following table represents the calculation of factors of 3584 in pairs:

Factor Pair Pair Factorization
1 and 3584 1 x 3584 = 3584
2 and 1792 2 x 1792 = 3584
4 and 896 4 x 896 = 3584
7 and 512 7 x 512 = 3584
8 and 448 8 x 448 = 3584
14 and 256 14 x 256 = 3584
16 and 224 16 x 224 = 3584
28 and 128 28 x 128 = 3584
32 and 112 32 x 112 = 3584
56 and 64 56 x 64 = 3584

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 3584. They are called negative pair factors.

Hence, the negative pairs of 3584 would be ( -1 , -3584 ) , ( -2 , -1792 ) , ( -4 , -896 ) , ( -7 , -512 ) , ( -8 , -448 ) , ( -14 , -256 ) , ( -16 , -224 ) , ( -28 , -128 ) , ( -32 , -112 ) and ( -56 , -64 ) .

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. 3584 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 3584.
  • Every number is a factor of zero (0), since 3584 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, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584 are exact divisors of 3584.
  • Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584. Each factor divides 3584 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584 are all less than or equal to 3584.

Frequently Asked Questions

  • What two numbers make 3584?

    Two numbers that make 3584 are 2 and 1792.

  • What is prime factorization of 3584?

    Prime factorization of 3584 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

  • Write some multiples of 3584?

    First five multiples of 3584 are 7168, 10752, 14336, 17920.

  • Which is the smallest prime factor of 3584?

    The smallest prime factor of 3584 is 2.

  • Is 3584 a perfect square?

    No 3584 is not a perfect square.

  • What is the sum of all factors of 3584?

    The sum of all factors of 3584 is 8184.

  • What are factors of 3584?

    Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.

  • How do you find factors of a negative number? ( eg. -3584 )?

    Factors of -3584 are -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -64, -112, -128, -224, -256, -448, -512, -896, -1792, -3584.

  • Is 3584 a whole number?

    Yes 3584 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 3584. Help him in finding the mean of 3584.

Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 3584 is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 64 + 112 + 128 + 224 + 256 + 448 + 512 + 896 + 1792 + 3584 = 8184.
Hence, the mean of factors of 3584 is 8184 ÷ 20 = 409.20.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3584? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -64, -112, -128, -224, -256, -448, -512, -896, -1792, -3584.

Joey wants to write all the prime factors of 3584 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3584 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 7.
So in exponential form it can be written as 29 x 7.

Kevin has been asked to write 19 factor(s) of 3584. Can you predict the answer?

19 factor(s) of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792.

Sammy is puzzled while calculating the prime factors of 3584. Can you help him find them?

Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
Prime factors of 3584 are 2, 2, 2, 2, 2, 2, 2, 2, 2, 7

What is prime factorization of 3584?

Prime factorization of 3584 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 = 29 x 7.

Can you help Rubel to find out the product of the even factors of 3584?

Factors of 3584 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
Even factors of 3584 are 2, 4, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 256, 448, 512, 896, 1792, 3584.
Hence, product of even factors of 3584 is; 2 x 4 x 8 x 14 x 16 x 28 x 32 x 56 x 64 x 112 x 128 x 224 x 256 x 448 x 512 x 896 x 1792 x 3584 = 4.99553458348868e+34.