# Factors of 1664

Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, and 1664

#### How to find factors of a number

 1.   Find factors of 1664 using Division Method 2.   Find factors of 1664 using Prime Factorization 3.   Find factors of 1664 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1664

• Divide 1664 by 1: 1664 ÷ 1 : Remainder = 0
• Divide 1664 by 2: 1664 ÷ 2 : Remainder = 0
• Divide 1664 by 4: 1664 ÷ 4 : Remainder = 0
• Divide 1664 by 8: 1664 ÷ 8 : Remainder = 0
• Divide 1664 by 13: 1664 ÷ 13 : Remainder = 0
• Divide 1664 by 16: 1664 ÷ 16 : Remainder = 0
• Divide 1664 by 26: 1664 ÷ 26 : Remainder = 0
• Divide 1664 by 32: 1664 ÷ 32 : Remainder = 0
• Divide 1664 by 52: 1664 ÷ 52 : Remainder = 0
• Divide 1664 by 64: 1664 ÷ 64 : Remainder = 0
• Divide 1664 by 104: 1664 ÷ 104 : Remainder = 0
• Divide 1664 by 128: 1664 ÷ 128 : Remainder = 0
• Divide 1664 by 208: 1664 ÷ 208 : Remainder = 0
• Divide 1664 by 416: 1664 ÷ 416 : Remainder = 0
• Divide 1664 by 832: 1664 ÷ 832 : Remainder = 0
• Divide 1664 by 1664: 1664 ÷ 1664 : Remainder = 0

Hence, Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, and 1664

#### 2. Steps to find factors of 1664 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 1664 using the division method, follow these steps:

• Step 1. Start dividing 1664 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 1664, which is 2. Divide 1664 by 2 to obtain the quotient (832).
1664 ÷ 2 = 832
• Step 3. Repeat step 1 with the obtained quotient (832).
832 ÷ 2 = 416
416 ÷ 2 = 208
208 ÷ 2 = 104
104 ÷ 2 = 52
52 ÷ 2 = 26
26 ÷ 2 = 13
13 ÷ 13 = 1

So, the prime factorization of 1664 is, 1664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1664 as shown below:

So, the prime factorization of 1664 is, 1664 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13.

#### 3. Find factors of 1664 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 1664 would be the two numbers which, when multiplied, give 1664 as the result.

The following table represents the calculation of factors of 1664 in pairs:

Factor Pair Pair Factorization
1 and 1664 1 x 1664 = 1664
2 and 832 2 x 832 = 1664
4 and 416 4 x 416 = 1664
8 and 208 8 x 208 = 1664
13 and 128 13 x 128 = 1664
16 and 104 16 x 104 = 1664
26 and 64 26 x 64 = 1664
32 and 52 32 x 52 = 1664

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 1664. They are called negative pair factors.

Hence, the negative pairs of 1664 would be ( -1 , -1664 ) , ( -2 , -832 ) , ( -4 , -416 ) , ( -8 , -208 ) , ( -13 , -128 ) , ( -16 , -104 ) , ( -26 , -64 ) and ( -32 , -52 ) .

#### 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. 1664 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1664.
• Every number is a factor of zero (0), since 1664 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, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 are exact divisors of 1664.
• Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664. Each factor divides 1664 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664 are all less than or equal to 1664.

• What is prime factorization of 1664?

Prime factorization of 1664 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13.

• How do you find factors of a negative number? ( eg. -1664 )?

Factors of -1664 are -1, -2, -4, -8, -13, -16, -26, -32, -52, -64, -104, -128, -208, -416, -832, -1664.

• What are the prime factors of 1664?

The factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Prime factors of 1664 are 2, 2, 2, 2, 2, 2, 2, 13.

• What are pair factors of 1664?

The pair factors of 1664 are (1,1664), (2,832), (4,416), (8,208), (13,128), (16,104), (26,64), (32,52).

• What is the greatest prime factors of 1664?

The greatest prime factor of 1664 is 13.

• What are six multiples of 1664?

First five multiples of 1664 are 3328, 4992, 6656, 8320, 9984, 11648.

• What are factors of 1664?

Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.

• Which is the smallest prime factor of 1664?

Smallest prime factor of 1664 is 2.

• Is 1664 a whole number?

Yes 1664 is a whole number.

#### Examples of Factors

Kevin has been asked to write 15 factor(s) of 1664. Can you predict the answer?

15 factor(s) of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832.

Sammy is puzzled while calculating the prime factors of 1664. Can you help him find them?

Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Prime factors of 1664 are 2, 2, 2, 2, 2, 2, 2, 13

What is prime factorization of 1664?

Prime factorization of 1664 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 13 = 27 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 1664. Can you help her?

Prime factors of 1664 are 2, 2, 2, 2, 2, 2, 2, 13.
Hence, the product of prime factors of 26.

Can you help Rubel to find out the product of the even factors of 1664?

Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Even factors of 1664 are 2, 4, 8, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Hence, product of even factors of 1664 is; 2 x 4 x 8 x 16 x 26 x 32 x 52 x 64 x 104 x 128 x 208 x 416 x 832 x 1664 = 4.52150716446802e+24.

Joy wants to calculate mean of all the factors of 1664. Help him in finding the mean of 1664.

Factors of 1664 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1664 is 1 + 2 + 4 + 8 + 13 + 16 + 26 + 32 + 52 + 64 + 104 + 128 + 208 + 416 + 832 + 1664 = 3570.
Hence, the mean of factors of 1664 is 3570 ÷ 16 = 223.13.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1664? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664.
Negative factors are -1, -2, -4, -8, -13, -16, -26, -32, -52, -64, -104, -128, -208, -416, -832, -1664.