# Factors of 174

Factors of 174 are 1, 2, 3, 6, 29, 58, 87, and 174

#### How to find factors of a number

 1.   Find factors of 174 using Division Method 2.   Find factors of 174 using Prime Factorization 3.   Find factors of 174 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 174

• Divide 174 by 1: 174 ÷ 1 : Remainder = 0
• Divide 174 by 2: 174 ÷ 2 : Remainder = 0
• Divide 174 by 3: 174 ÷ 3 : Remainder = 0
• Divide 174 by 6: 174 ÷ 6 : Remainder = 0
• Divide 174 by 29: 174 ÷ 29 : Remainder = 0
• Divide 174 by 58: 174 ÷ 58 : Remainder = 0
• Divide 174 by 87: 174 ÷ 87 : Remainder = 0
• Divide 174 by 174: 174 ÷ 174 : Remainder = 0

Hence, Factors of 174 are 1, 2, 3, 6, 29, 58, 87, and 174

#### 2. Steps to find factors of 174 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 174 using the division method, follow these steps:

• Step 1. Start dividing 174 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 174, which is 2. Divide 174 by 2 to obtain the quotient (87).
174 ÷ 2 = 87
• Step 3. Repeat step 1 with the obtained quotient (87).
87 ÷ 3 = 29
29 ÷ 29 = 1

So, the prime factorization of 174 is, 174 = 2 x 3 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 174 as shown below:

So, the prime factorization of 174 is, 174 = 2 x 3 x 29.

#### 3. Find factors of 174 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 174 would be the two numbers which, when multiplied, give 174 as the result.

The following table represents the calculation of factors of 174 in pairs:

Factor Pair Pair Factorization
1 and 174 1 x 174 = 174
2 and 87 2 x 87 = 174
3 and 58 3 x 58 = 174
6 and 29 6 x 29 = 174

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 174. They are called negative pair factors.

Hence, the negative pairs of 174 would be ( -1 , -174 ) , ( -2 , -87 ) , ( -3 , -58 ) and ( -6 , -29 ) .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 174 is a factor of itself.
• 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, 3, 6, 29, 58, 87, 174 are exact divisors of 174.
• 1 is a factor of every number. Eg. 1 is a factor of 174.
• Every number is a factor of zero (0), since 174 x 0 = 0.

• What are the prime factors of 174?

The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Prime factors of 174 are 2, 3, 29.

• What two numbers make 174?

Two numbers that make 174 are 2 and 87.

• What is the greatest prime factors of 174?

The greatest prime factor of 174 is 29.

• What are factors of 174?

Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.

• How do you find factors of a negative number? ( eg. -174 )?

Factors of -174 are -1, -2, -3, -6, -29, -58, -87, -174.

• What are five multiples of 174?

First five multiples of 174 are 348, 522, 696, 870, 1044.

• Write some multiples of 174?

First five multiples of 174 are 348, 522, 696, 870.

• Is 174 a perfect square?

No 174 is not a perfect square.

• What two numbers make 174?

Two numbers that make 174 are 2 and 87.

#### Examples of Factors

What is prime factorization of 174?

Prime factorization of 174 is 2 x 3 x 29 = 2 x 3 x 29.

Sammy is puzzled while calculating the prime factors of 174. Can you help him find them?

Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Prime factors of 174 are 2, 3, 29

Kevin has been asked to write 7 factor(s) of 174. Can you predict the answer?

7 factor(s) of 174 are 1, 2, 3, 6, 29, 58, 87.

Joey wants to write all the prime factors of 174 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 174 are 2, 3, 29.
So in exponential form it can be written as 2 x 3 x 29.

How many factors are there for 174?

Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 174? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 29, 58, 87, 174.
Negative factors are -1, -2, -3, -6, -29, -58, -87, -174.

Can you help Rubel to find out the product of the even factors of 174?

Factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174.
Even factors of 174 are 2, 6, 58, 174.
Hence, product of even factors of 174 is; 2 x 6 x 58 x 174 = 121104.