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 = 2⁴ × 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 upside-down 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?

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.