# Factors of 3136

Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, and 3136

#### How to find factors of a number

 1.   Find factors of 3136 using Division Method 2.   Find factors of 3136 using Prime Factorization 3.   Find factors of 3136 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 3136

• Divide 3136 by 1: 3136 ÷ 1 : Remainder = 0
• Divide 3136 by 2: 3136 ÷ 2 : Remainder = 0
• Divide 3136 by 4: 3136 ÷ 4 : Remainder = 0
• Divide 3136 by 7: 3136 ÷ 7 : Remainder = 0
• Divide 3136 by 8: 3136 ÷ 8 : Remainder = 0
• Divide 3136 by 14: 3136 ÷ 14 : Remainder = 0
• Divide 3136 by 16: 3136 ÷ 16 : Remainder = 0
• Divide 3136 by 28: 3136 ÷ 28 : Remainder = 0
• Divide 3136 by 32: 3136 ÷ 32 : Remainder = 0
• Divide 3136 by 49: 3136 ÷ 49 : Remainder = 0
• Divide 3136 by 56: 3136 ÷ 56 : Remainder = 0
• Divide 3136 by 64: 3136 ÷ 64 : Remainder = 0
• Divide 3136 by 98: 3136 ÷ 98 : Remainder = 0
• Divide 3136 by 112: 3136 ÷ 112 : Remainder = 0
• Divide 3136 by 196: 3136 ÷ 196 : Remainder = 0
• Divide 3136 by 224: 3136 ÷ 224 : Remainder = 0
• Divide 3136 by 392: 3136 ÷ 392 : Remainder = 0
• Divide 3136 by 448: 3136 ÷ 448 : Remainder = 0
• Divide 3136 by 784: 3136 ÷ 784 : Remainder = 0
• Divide 3136 by 1568: 3136 ÷ 1568 : Remainder = 0
• Divide 3136 by 3136: 3136 ÷ 3136 : Remainder = 0

Hence, Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, and 3136

#### 2. Steps to find factors of 3136 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 3136 using the division method, follow these steps:

• Step 1. Start dividing 3136 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 3136, which is 2. Divide 3136 by 2 to obtain the quotient (1568).
3136 ÷ 2 = 1568
• Step 3. Repeat step 1 with the obtained quotient (1568).
1568 ÷ 2 = 784
784 ÷ 2 = 392
392 ÷ 2 = 196
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 3136 is, 3136 = 2 x 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 3136 as shown below:

So, the prime factorization of 3136 is, 3136 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7.

#### 3. Find factors of 3136 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 3136 would be the two numbers which, when multiplied, give 3136 as the result.

The following table represents the calculation of factors of 3136 in pairs:

Factor Pair Pair Factorization
1 and 3136 1 x 3136 = 3136
2 and 1568 2 x 1568 = 3136
4 and 784 4 x 784 = 3136
7 and 448 7 x 448 = 3136
8 and 392 8 x 392 = 3136
14 and 224 14 x 224 = 3136
16 and 196 16 x 196 = 3136
28 and 112 28 x 112 = 3136
32 and 98 32 x 98 = 3136
49 and 64 49 x 64 = 3136
56 and 56 56 x 56 = 3136

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 3136. They are called negative pair factors.

Hence, the negative pairs of 3136 would be ( -1 , -3136 ) , ( -2 , -1568 ) , ( -4 , -784 ) , ( -7 , -448 ) , ( -8 , -392 ) , ( -14 , -224 ) , ( -16 , -196 ) , ( -28 , -112 ) , ( -32 , -98 ) , ( -49 , -64 ) and ( -56 , -56 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 3136 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 3136.
• Every number is a factor of zero (0), since 3136 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, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 are exact divisors of 3136.
• Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136. Each factor divides 3136 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, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136 are all less than or equal to 3136.

• Is 3136 a perfect square?

Yes 3136 is a perfect square.

• What are factors of 3136?

Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.

• Which is greatest factor of 3136?

The greatest factor of 3136 is 1568.

• What is the sum of all factors of 3136?

The sum of all factors of 3136 is 7239.

• What are multiples of 3136?

First five multiples of 3136 are 6272, 9408, 12544, 15680.

• What is the greatest prime factors of 3136?

The greatest prime factor of 3136 is 7.

• What are six multiples of 3136?

First five multiples of 3136 are 6272, 9408, 12544, 15680, 18816, 21952.

• What is prime factorization of 3136?

Prime factorization of 3136 is 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7.

• Is 3136 a whole number?

Yes 3136 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 3136? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -32, -49, -56, -64, -98, -112, -196, -224, -392, -448, -784, -1568, -3136.

Can you help Sammy find out the product of the odd factors of 3136?

Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.
Odd factors of 3136 are 1, 7, 49.
Hence product of odd factors of 3136 is; 1 x 7 x 49 = 343.

Joey wants to write all the prime factors of 3136 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 3136 are 2, 2, 2, 2, 2, 2, 7, 7.
So in exponential form it can be written as 26 x 72.

How many factors are there for 3136?

Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.
So there are in total 21 factors.

Kevin has been asked to write 20 factor(s) of 3136. Can you predict the answer?

20 factor(s) of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568.

Sammy is puzzled while calculating the prime factors of 3136. Can you help him find them?

Factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136.
Prime factors of 3136 are 2, 2, 2, 2, 2, 2, 7, 7

What is prime factorization of 3136?

Prime factorization of 3136 is 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 = 26 x 72.