# Factors of 176

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

#### How to find factors of a number

 1.   Find factors of 176 using Division Method 2.   Find factors of 176 using Prime Factorization 3.   Find factors of 176 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 176

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

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

#### 2. Steps to find factors of 176 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 176 using the division method, follow these steps:

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

So, the prime factorization of 176 is, 176 = 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 176 as shown below:

So, the prime factorization of 176 is, 176 = 2 x 2 x 2 x 2 x 11.

#### 3. Find factors of 176 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 176 would be the two numbers which, when multiplied, give 176 as the result.

The following table represents the calculation of factors of 176 in pairs:

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

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 176. They are called negative pair factors.

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

#### 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. 176 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 176.
• Every number is a factor of zero (0), since 176 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, 44, 88, 176 are exact divisors of 176.
• Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176. Each factor divides 176 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, 44, 88, 176 are all less than or equal to 176.

• What are the pair factors of 176?

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

• What are five multiples of 176?

First five multiples of 176 are 352, 528, 704, 880, 1056.

• What two numbers make 176?

Two numbers that make 176 are 2 and 88.

• What is the sum of all factors of 176?

The sum of all factors of 176 is 372.

• What are factors of -176?

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

• What are factors of 176?

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

• Is 176 a perfect square?

No 176 is not a perfect square.

• Which is the smallest prime factor of 176?

Smallest prime factor of 176 is 2.

• Which is greatest factor of 176?

The greatest factor of 176 is 88.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 176?

Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176.
Odd factors of 176 are 1, 11.
Hence product of odd factors of 176 is; 1 x 11 = 11.

Joey wants to write all the prime factors of 176 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 176 are 2, 2, 2, 2, 11.
So in exponential form it can be written as 24 x 11.

How many factors are there for 176?

Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176.
So there are in total 10 factors.

Kevin has been asked to write 9 factor(s) of 176. Can you predict the answer?

9 factor(s) of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88.

Sammy is puzzled while calculating the prime factors of 176. Can you help him find them?

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

What is prime factorization of 176?

Prime factorization of 176 is 2 x 2 x 2 x 2 x 11 = 24 x 11.

Can you help Rubel to find out the product of the even factors of 176?

Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176.
Even factors of 176 are 2, 4, 8, 16, 22, 44, 88, 176.
Hence, product of even factors of 176 is; 2 x 4 x 8 x 16 x 22 x 44 x 88 x 176 = 15352201216.