# Factors of 374

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374

#### How to find factors of a number

 1.   Find factors of 374 using Division Method 2.   Find factors of 374 using Prime Factorization 3.   Find factors of 374 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 374

• Divide 374 by 1: 374 ÷ 1 : Remainder = 0
• Divide 374 by 2: 374 ÷ 2 : Remainder = 0
• Divide 374 by 11: 374 ÷ 11 : Remainder = 0
• Divide 374 by 17: 374 ÷ 17 : Remainder = 0
• Divide 374 by 22: 374 ÷ 22 : Remainder = 0
• Divide 374 by 34: 374 ÷ 34 : Remainder = 0
• Divide 374 by 187: 374 ÷ 187 : Remainder = 0
• Divide 374 by 374: 374 ÷ 374 : Remainder = 0

Hence, Factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374

#### 2. Steps to find factors of 374 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 374 using the division method, follow these steps:

• Step 1. Start dividing 374 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 374, which is 2. Divide 374 by 2 to obtain the quotient (187).
374 ÷ 2 = 187
• Step 3. Repeat step 1 with the obtained quotient (187).
187 ÷ 11 = 17
17 ÷ 17 = 1

So, the prime factorization of 374 is, 374 = 2 x 11 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 374 as shown below:

So, the prime factorization of 374 is, 374 = 2 x 11 x 17.

#### 3. Find factors of 374 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 374 would be the two numbers which, when multiplied, give 374 as the result.

The following table represents the calculation of factors of 374 in pairs:

Factor Pair Pair Factorization
1 and 374 1 x 374 = 374
2 and 187 2 x 187 = 374
11 and 34 11 x 34 = 374
17 and 22 17 x 22 = 374

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 374. They are called negative pair factors.

Hence, the negative pairs of 374 would be ( -1 , -374 ) , ( -2 , -187 ) , ( -11 , -34 ) and ( -17 , -22 ) .

#### 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. 374 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, 11, 17, 22, 34, 187, 374 are exact divisors of 374.
• 1 is a factor of every number. Eg. 1 is a factor of 374.
• Every number is a factor of zero (0), since 374 x 0 = 0.

• What are the pair factors of 374?

Pair factors of 374 are (1,374), (2,187), (11,34), (17,22).

• What are five multiples of 374?

First five multiples of 374 are 748, 1122, 1496, 1870, 2244.

• What two numbers make 374?

Two numbers that make 374 are 2 and 187.

• What is the sum of all factors of 374?

The sum of all factors of 374 is 648.

• What are factors of -374?

Factors of -374 are -1, -2, -11, -17, -22, -34, -187, -374.

• What are factors of 374?

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374.

• Is 374 a perfect square?

No 374 is not a perfect square.

• Which is the smallest prime factor of 374?

Smallest prime factor of 374 is 2.

• Which is greatest factor of 374?

The greatest factor of 374 is 187.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 374?

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374.
Odd factors of 374 are 1, 11, 17, 187.
Hence product of odd factors of 374 is; 1 x 11 x 17 x 187 = 34969.

Joey wants to write all the prime factors of 374 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 374 are 2, 11, 17.
So in exponential form it can be written as 2 x 11 x 17.

How many factors are there for 374?

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 374. Can you predict the answer?

7 factor(s) of 374 are 1, 2, 11, 17, 22, 34, 187.

Sammy is puzzled while calculating the prime factors of 374. Can you help him find them?

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374.
Prime factors of 374 are 2, 11, 17

What is prime factorization of 374?

Prime factorization of 374 is 2 x 11 x 17 = 2 x 11 x 17.

Can you help Rubel to find out the product of the even factors of 374?

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374.
Even factors of 374 are 2, 22, 34, 374.
Hence, product of even factors of 374 is; 2 x 22 x 34 x 374 = 559504.