# Factors of 1568

Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, and 1568

#### How to find factors of a number

 1.   Find factors of 1568 using Division Method 2.   Find factors of 1568 using Prime Factorization 3.   Find factors of 1568 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1568

• Divide 1568 by 1: 1568 ÷ 1 : Remainder = 0
• Divide 1568 by 2: 1568 ÷ 2 : Remainder = 0
• Divide 1568 by 4: 1568 ÷ 4 : Remainder = 0
• Divide 1568 by 7: 1568 ÷ 7 : Remainder = 0
• Divide 1568 by 8: 1568 ÷ 8 : Remainder = 0
• Divide 1568 by 14: 1568 ÷ 14 : Remainder = 0
• Divide 1568 by 16: 1568 ÷ 16 : Remainder = 0
• Divide 1568 by 28: 1568 ÷ 28 : Remainder = 0
• Divide 1568 by 32: 1568 ÷ 32 : Remainder = 0
• Divide 1568 by 49: 1568 ÷ 49 : Remainder = 0
• Divide 1568 by 56: 1568 ÷ 56 : Remainder = 0
• Divide 1568 by 98: 1568 ÷ 98 : Remainder = 0
• Divide 1568 by 112: 1568 ÷ 112 : Remainder = 0
• Divide 1568 by 196: 1568 ÷ 196 : Remainder = 0
• Divide 1568 by 224: 1568 ÷ 224 : Remainder = 0
• Divide 1568 by 392: 1568 ÷ 392 : Remainder = 0
• Divide 1568 by 784: 1568 ÷ 784 : Remainder = 0
• Divide 1568 by 1568: 1568 ÷ 1568 : Remainder = 0

Hence, Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, and 1568

#### 2. Steps to find factors of 1568 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 1568 using the division method, follow these steps:

• Step 1. Start dividing 1568 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 1568, which is 2. Divide 1568 by 2 to obtain the quotient (784).
1568 ÷ 2 = 784
• Step 3. Repeat step 1 with the obtained quotient (784).
784 ÷ 2 = 392
392 ÷ 2 = 196
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 1568 is, 1568 = 2 x 2 x 2 x 2 x 2 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1568 as shown below:

So, the prime factorization of 1568 is, 1568 = 2 x 2 x 2 x 2 x 2 x 7 x 7.

#### 3. Find factors of 1568 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 1568 would be the two numbers which, when multiplied, give 1568 as the result.

The following table represents the calculation of factors of 1568 in pairs:

Factor Pair Pair Factorization
1 and 1568 1 x 1568 = 1568
2 and 784 2 x 784 = 1568
4 and 392 4 x 392 = 1568
7 and 224 7 x 224 = 1568
8 and 196 8 x 196 = 1568
14 and 112 14 x 112 = 1568
16 and 98 16 x 98 = 1568
28 and 56 28 x 56 = 1568
32 and 49 32 x 49 = 1568

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 1568. They are called negative pair factors.

Hence, the negative pairs of 1568 would be ( -1 , -1568 ) , ( -2 , -784 ) , ( -4 , -392 ) , ( -7 , -224 ) , ( -8 , -196 ) , ( -14 , -112 ) , ( -16 , -98 ) , ( -28 , -56 ) and ( -32 , -49 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1568 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1568.
• Every number is a factor of zero (0), since 1568 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, 49, 56, 98, 112, 196, 224, 392, 784, 1568 are exact divisors of 1568.
• Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568. Each factor divides 1568 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, 49, 56, 98, 112, 196, 224, 392, 784, 1568 are all less than or equal to 1568.

• What two numbers make 1568?

Two numbers that make 1568 are 2 and 784.

• What is prime factorization of 1568?

Prime factorization of 1568 is 2 x 2 x 2 x 2 x 2 x 7 x 7.

• Write some multiples of 1568?

First five multiples of 1568 are 3136, 4704, 6272, 7840.

• Which is the smallest prime factor of 1568?

The smallest prime factor of 1568 is 2.

• Is 1568 a perfect square?

No 1568 is not a perfect square.

• What is the sum of all factors of 1568?

The sum of all factors of 1568 is 3591.

• What are factors of 1568?

Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568.

• How do you find factors of a negative number? ( eg. -1568 )?

Factors of -1568 are -1, -2, -4, -7, -8, -14, -16, -28, -32, -49, -56, -98, -112, -196, -224, -392, -784, -1568.

• Is 1568 a whole number?

Yes 1568 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 1568. Help him in finding the mean of 1568.

Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 1568 is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 49 + 56 + 98 + 112 + 196 + 224 + 392 + 784 + 1568 = 3591.
Hence, the mean of factors of 1568 is 3591 ÷ 18 = 199.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1568? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -32, -49, -56, -98, -112, -196, -224, -392, -784, -1568.

Joey wants to write all the prime factors of 1568 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1568 are 2, 2, 2, 2, 2, 7, 7.
So in exponential form it can be written as 25 x 72.

Kevin has been asked to write 17 factor(s) of 1568. Can you predict the answer?

17 factor(s) of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784.

Sammy is puzzled while calculating the prime factors of 1568. Can you help him find them?

Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568.
Prime factors of 1568 are 2, 2, 2, 2, 2, 7, 7

What is prime factorization of 1568?

Prime factorization of 1568 is 2 x 2 x 2 x 2 x 2 x 7 x 7 = 25 x 72.

Can you help Rubel to find out the product of the even factors of 1568?

Factors of 1568 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568.
Even factors of 1568 are 2, 4, 8, 14, 16, 28, 32, 56, 98, 112, 196, 224, 392, 784, 1568.
Hence, product of even factors of 1568 is; 2 x 4 x 8 x 14 x 16 x 28 x 32 x 56 x 98 x 112 x 196 x 224 x 392 x 784 x 1568 = 1.670399706804516e+26.