Factors of 176
The factors of 176, are the integers which when multiplied with another integer give the result in the number 176. There are a total of 5 pairs of numbers or 10 factors that give us the factors of 176. In this lesson, we will calculate the factors of 176, prime factors of 176, and factors of 176 in pairs along with solved examples for a better understanding.
 Factors of 176: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176.
 Prime Factorization of 176: 176 = 2^{4} × 11
What are the Factors of 176?
A factor is a number which divides the given number without leaving a remainder, so the numbers which gives the remainder as 0 when divided by 176 will be the factors of 176. 176 ÷ 2 = 88. Here we get the quotient 88 and the remainder is 0. Hence 2 and 88 are the factors of 176. There are a total 10 factors of 176. The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
How to Calculate the Factors of 176?
The division method can be used to find the factors of 176. In the division method, we find the numbers which divide 176 exactly without leaving a remainder.
Factors of 176 by Division Method
We should divide 176 by natural numbers and see which all numbers exactly divides 176 and bring 0 as a remainder for getting the factors of 176. Let us try dividing 176 by 2, 4, 8 and see if they are exactly divisible. They are divisible so they are factors of 176. Similarly, 11, 16, 22, 44, 88, and 176 are also factors of 176. Just try dividing 176 by using the different numbers. At the same time, if we take numbers like 3, 7, and 9 in a random way, we can see that they are not exactly divisible. Now, we can have 3, 7, and 9 leaves remainders. So they are not factors of 176.
Explore factors using illustrations and interactive examples.
 Factors of 69: The factors of 69 are 1, 3, 23, 69.
 Factors of 49  The factors of 49 are 1, 7, 49
 Factors of 96  The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
 Factors of 264  The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264.
 Factors of 216  The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108
, and 216 ·  Factors of 900  The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450
Factors of 176 by Prime Factorization
Dividing number 176 by prime numbers and seeing if it does not leave any remainder and continuing the division with the quotient is called the prime factorization method. Then we express 176 as a product of its prime factors. We can find the prime factors by the division method or prime factorization method.
1. Prime Factorization of 176 by Division Method
176 is divided by the smallest prime number which divides 176 exactly. The quotient thus obtained is then divided by the smallest or second smallest prime number and the process continues till the quotient gets undividable. Let us divide 176 by the smallest prime number 2
 176 ÷ 2 = 88
 88 ÷ 2 = 44
 44 ÷ 2 = 22
 22 ÷ 2 = 11
 11 ÷ 11 = 1
Now, we get a prime number as the result, that cannot be divided further. Therefore the prime factorization of 176 is 176 =2 × 2 × 2 × 2 × 11.
2. Prime Factorization of 90 by Upside Down Division Method
This method is called the upsidedown division method because the division symbol is flipped upside down. Here we divide 176 by the prime number 2. We continue to do this till we get a prime number as the result, as shown below:
Now, it cannot be further divided. Therefore prime factorization of 176 is 2 × 2 × 2 × 2 × 11.
The set of two numbers when multiplied will get a product is called pair factors. Pair factors of 176 are
 1 × 176 = 176
 2 × 88 = 176
 4 × 44 = 176
 8 × 22 = 176
 11 × 16 = 176
 The factors of 176 in pairs are (1, 176), (2, 88), (4, 44), (8, 22), and (11, 16).
 There can be negative pair factors also (1, 176), (2, 88), (4, 44), (8, 22), and (11, 16).
Important Notes:
 Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
 There are negative pair factors of 176
 Prime factorization can be done by the division method, factor tree method, and upside down division method.
Challenging Questions:
 Find the prime factors of 176 by the factor tree method?
 What is the sum of all the even factors of 176?
Factors of 176 Solved Examples

Example 1: The class teacher asked the students to donate some amount to the school program. If there are 44 students in a class and each student donates $4 then, calculate the total amount donated by students?
Solution:
Total number of students = 44
Each student donates = $4
With the help of factors of 176 we calculated the total amount = 44 × 4 = $176
The total amount of $176 is to be donated. 
Example 2: Alvin is asked in his homework to write down all the positive factor pairs of 176. Help Alvin in listing the same.
Solution:
Alvin's answer will be
 1 × 176 = 176
 2 × 88 = 176
 4 × 44 = 176
 8 × 22 = 176
 11 × 16 = 176
Therefore pair factors of 176 are (1, 176), (2, 88), (4, 44), (8, 22), and (11, 16).

Example 3: Christ wants to find out the product of the odd factors of 176. Can you assist Christ?
Solution:
Factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
Odd factors of 176 are 1 and 11
Product of odd factors of 176 is 1 × 11 = 11
FAQs on Factors of 176
What are the factors of 176?
The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
What is the smallest factor of 176?
The smallest factor of 176 is 1.
What are the negative factors of 176?
Negative factors of 176 are 1,  2,  4,  8,  11, 16,  22,  44,  88, and  176.
What are the prime factors of 176?
The prime factors of 176 are 2 and 11.
What are the common factors of 176 and 76?
Factors of 176 = 1, 2, 4, 8, 11, 16, 22, 44, 88, and 176.
Factors of 76 = 1, 2, 4, 19, 38, and 76
The common factors of 176 and 76 are 1, 2, and 4.
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