# Factors of 352

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352

#### How to find factors of a number

 1.   Find factors of 352 using Division Method 2.   Find factors of 352 using Prime Factorization 3.   Find factors of 352 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 352

• Divide 352 by 1: 352 ÷ 1 : Remainder = 0
• Divide 352 by 2: 352 ÷ 2 : Remainder = 0
• Divide 352 by 4: 352 ÷ 4 : Remainder = 0
• Divide 352 by 8: 352 ÷ 8 : Remainder = 0
• Divide 352 by 11: 352 ÷ 11 : Remainder = 0
• Divide 352 by 16: 352 ÷ 16 : Remainder = 0
• Divide 352 by 22: 352 ÷ 22 : Remainder = 0
• Divide 352 by 32: 352 ÷ 32 : Remainder = 0
• Divide 352 by 44: 352 ÷ 44 : Remainder = 0
• Divide 352 by 88: 352 ÷ 88 : Remainder = 0
• Divide 352 by 176: 352 ÷ 176 : Remainder = 0
• Divide 352 by 352: 352 ÷ 352 : Remainder = 0

Hence, Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352

#### 2. Steps to find factors of 352 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 352 using the division method, follow these steps:

• Step 1. Start dividing 352 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 352, which is 2. Divide 352 by 2 to obtain the quotient (176).
352 ÷ 2 = 176
• Step 3. Repeat step 1 with the obtained quotient (176).
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1

So, the prime factorization of 352 is, 352 = 2 x 2 x 2 x 2 x 2 x 11.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 352 as shown below:

So, the prime factorization of 352 is, 352 = 2 x 2 x 2 x 2 x 2 x 11.

#### 3. Find factors of 352 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 352 would be the two numbers which, when multiplied, give 352 as the result.

The following table represents the calculation of factors of 352 in pairs:

Factor Pair Pair Factorization
1 and 352 1 x 352 = 352
2 and 176 2 x 176 = 352
4 and 88 4 x 88 = 352
8 and 44 8 x 44 = 352
11 and 32 11 x 32 = 352
16 and 22 16 x 22 = 352

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 352. They are called negative pair factors.

Hence, the negative pairs of 352 would be ( -1 , -352 ) , ( -2 , -176 ) , ( -4 , -88 ) , ( -8 , -44 ) , ( -11 , -32 ) and ( -16 , -22 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 352 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 352.
• Every number is a factor of zero (0), since 352 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, 11, 16, 22, 32, 44, 88, 176, 352 are exact divisors of 352.
• Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352. Each factor divides 352 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352 are all less than or equal to 352.

• What are the prime factors of 352?

The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
Prime factors of 352 are 2, 2, 2, 2, 2, 11.

• What is the sum of all factors of 352?

The sum of all factors of 352 is 756.

• What are the pair factors of 352?

Pair factors of 352 are (1,352), (2,176), (4,88), (8,44), (11,32), (16,22).

• What two numbers make 352?

Two numbers that make 352 are 2 and 176.

• What are multiples of 352?

First five multiples of 352 are 704, 1056, 1408, 1760.

• Is 352 a perfect square?

No 352 is not a perfect square.

• Which is greatest factor of 352?

The greatest factor of 352 is 176.

• How do you factors of 352?

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.

• What are five multiples of 352?

First five multiples of 352 are 704, 1056, 1408, 1760, 2112.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 352?

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
Even factors of 352 are 2, 4, 8, 16, 22, 32, 44, 88, 176, 352.
Hence, product of even factors of 352 is; 2 x 4 x 8 x 16 x 22 x 32 x 44 x 88 x 176 x 352 = 172927194497024.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 352? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
Negative factors are -1, -2, -4, -8, -11, -16, -22, -32, -44, -88, -176, -352.

How many factors are there for 352?

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
So there are in total 12 factors.

Sammy is puzzled while calculating the prime factors of 352. Can you help him find them?

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
Prime factors of 352 are 2, 2, 2, 2, 2, 11

Joey wants to write all the prime factors of 352 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 352 are 2, 2, 2, 2, 2, 11.
So in exponential form it can be written as 25 x 11.

What is prime factorization of 352?

Prime factorization of 352 is 2 x 2 x 2 x 2 x 2 x 11 = 25 x 11.

Can you help Rubel to find out the product of the even factors of 352?

Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352.
Even factors of 352 are 2, 4, 8, 16, 22, 32, 44, 88, 176, 352.
Hence, product of even factors of 352 is; 2 x 4 x 8 x 16 x 22 x 32 x 44 x 88 x 176 x 352 = 172927194497024.