# Factors of 172

Factors of 172 are 1, 2, 4, 43, 86, and 172

#### How to find factors of a number

 1.   Find factors of 172 using Division Method 2.   Find factors of 172 using Prime Factorization 3.   Find factors of 172 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 172

• Divide 172 by 1: 172 ÷ 1 : Remainder = 0
• Divide 172 by 2: 172 ÷ 2 : Remainder = 0
• Divide 172 by 4: 172 ÷ 4 : Remainder = 0
• Divide 172 by 43: 172 ÷ 43 : Remainder = 0
• Divide 172 by 86: 172 ÷ 86 : Remainder = 0
• Divide 172 by 172: 172 ÷ 172 : Remainder = 0

Hence, Factors of 172 are 1, 2, 4, 43, 86, and 172

#### 2. Steps to find factors of 172 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 172 using the division method, follow these steps:

• Step 1. Start dividing 172 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 172, which is 2. Divide 172 by 2 to obtain the quotient (86).
172 ÷ 2 = 86
• Step 3. Repeat step 1 with the obtained quotient (86).
86 ÷ 2 = 43
43 ÷ 43 = 1

So, the prime factorization of 172 is, 172 = 2 x 2 x 43.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 172 as shown below:

So, the prime factorization of 172 is, 172 = 2 x 2 x 43.

#### 3. Find factors of 172 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 172 would be the two numbers which, when multiplied, give 172 as the result.

The following table represents the calculation of factors of 172 in pairs:

Factor Pair Pair Factorization
1 and 172 1 x 172 = 172
2 and 86 2 x 86 = 172
4 and 43 4 x 43 = 172

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 172. They are called negative pair factors.

Hence, the negative pairs of 172 would be ( -1 , -172 ) , ( -2 , -86 ) and ( -4 , -43 ) .

#### 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. 172 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 172.
• Every number is a factor of zero (0), since 172 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, 43, 86, 172 are exact divisors of 172.
• Factors of 172 are 1, 2, 4, 43, 86, 172. Each factor divides 172 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 43, 86, 172 are all less than or equal to 172.

• What are the prime factors of 172?

The factors of 172 are 1, 2, 4, 43, 86, 172.
Prime factors of 172 are 2, 2, 43.

• What is the sum of all factors of 172?

The sum of all factors of 172 is 308.

• What are the pair factors of 172?

Pair factors of 172 are (1,172), (2,86), (4,43).

• What two numbers make 172?

Two numbers that make 172 are 2 and 86.

• What are multiples of 172?

First five multiples of 172 are 344, 516, 688, 860.

• Is 172 a perfect square?

No 172 is not a perfect square.

• Which is greatest factor of 172?

The greatest factor of 172 is 86.

• How do you factors of 172?

Factors of 172 are 1, 2, 4, 43, 86, 172.

• What are five multiples of 172?

First five multiples of 172 are 344, 516, 688, 860, 1032.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 172?

Factors of 172 are 1, 2, 4, 43, 86, 172.
Even factors of 172 are 2, 4, 86, 172.
Hence, product of even factors of 172 is; 2 x 4 x 86 x 172 = 118336.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 172? Help her in writing all the factors.

Positive factors are 1, 2, 4, 43, 86, 172.
Negative factors are -1, -2, -4, -43, -86, -172.

How many factors are there for 172?

Factors of 172 are 1, 2, 4, 43, 86, 172.
So there are in total 6 factors.

Sammy is puzzled while calculating the prime factors of 172. Can you help him find them?

Factors of 172 are 1, 2, 4, 43, 86, 172.
Prime factors of 172 are 2, 2, 43

Joey wants to write all the prime factors of 172 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 172 are 2, 2, 43.
So in exponential form it can be written as 22 x 43.

What is prime factorization of 172?

Prime factorization of 172 is 2 x 2 x 43 = 22 x 43.

Can you help Rubel to find out the product of the even factors of 172?

Factors of 172 are 1, 2, 4, 43, 86, 172.
Even factors of 172 are 2, 4, 86, 172.
Hence, product of even factors of 172 is; 2 x 4 x 86 x 172 = 118336.