# Factors of 348

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348

#### How to find factors of a number

 1.   Find factors of 348 using Division Method 2.   Find factors of 348 using Prime Factorization 3.   Find factors of 348 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 348

• Divide 348 by 1: 348 ÷ 1 : Remainder = 0
• Divide 348 by 2: 348 ÷ 2 : Remainder = 0
• Divide 348 by 3: 348 ÷ 3 : Remainder = 0
• Divide 348 by 4: 348 ÷ 4 : Remainder = 0
• Divide 348 by 6: 348 ÷ 6 : Remainder = 0
• Divide 348 by 12: 348 ÷ 12 : Remainder = 0
• Divide 348 by 29: 348 ÷ 29 : Remainder = 0
• Divide 348 by 58: 348 ÷ 58 : Remainder = 0
• Divide 348 by 87: 348 ÷ 87 : Remainder = 0
• Divide 348 by 116: 348 ÷ 116 : Remainder = 0
• Divide 348 by 174: 348 ÷ 174 : Remainder = 0
• Divide 348 by 348: 348 ÷ 348 : Remainder = 0

Hence, Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, and 348

#### 2. Steps to find factors of 348 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 348 using the division method, follow these steps:

• Step 1. Start dividing 348 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 348, which is 2. Divide 348 by 2 to obtain the quotient (174).
348 ÷ 2 = 174
• Step 3. Repeat step 1 with the obtained quotient (174).
174 ÷ 2 = 87
87 ÷ 3 = 29
29 ÷ 29 = 1

So, the prime factorization of 348 is, 348 = 2 x 2 x 3 x 29.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 348 as shown below:

So, the prime factorization of 348 is, 348 = 2 x 2 x 3 x 29.

#### 3. Find factors of 348 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 348 would be the two numbers which, when multiplied, give 348 as the result.

The following table represents the calculation of factors of 348 in pairs:

Factor Pair Pair Factorization
1 and 348 1 x 348 = 348
2 and 174 2 x 174 = 348
3 and 116 3 x 116 = 348
4 and 87 4 x 87 = 348
6 and 58 6 x 58 = 348
12 and 29 12 x 29 = 348

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 348. They are called negative pair factors.

Hence, the negative pairs of 348 would be ( -1 , -348 ) , ( -2 , -174 ) , ( -3 , -116 ) , ( -4 , -87 ) , ( -6 , -58 ) and ( -12 , -29 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 348 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 348.
• Every number is a factor of zero (0), since 348 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, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 are exact divisors of 348.
• Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348. Each factor divides 348 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348 are all less than or equal to 348.

• How do you find factors of a negative number? ( eg. -348 )?

Factors of -348 are -1, -2, -3, -4, -6, -12, -29, -58, -87, -116, -174, -348.

• What is the sum of all factors of 348?

The sum of all factors of 348 is 840.

• What is prime factorization of 348?

Prime factorization of 348 is 2 x 2 x 3 x 29.

• What are the pair factors of 348?

Pair factors of 348 are (1,348), (2,174), (3,116), (4,87), (6,58), (12,29).

• What are six multiples of 348?

First five multiples of 348 are 696, 1044, 1392, 1740, 2088, 2436.

• Is 348 a whole number?

Yes 348 is a whole number.

• Which is the smallest prime factor of 348?

Smallest prime factor of 348 is 2.

• What are five multiples of 348?

First five multiples of 348 are 696, 1044, 1392, 1740, 2088.

• Write all factors of 348?

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.

#### Examples of Factors

Joey wants to write all the prime factors of 348 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 348 are 2, 2, 3, 29.
So in exponential form it can be written as 22 x 3 x 29.

How many factors are there for 348?

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 348. Can you predict the answer?

11 factor(s) of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174.

Sammy is puzzled while calculating the prime factors of 348. Can you help him find them?

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.
Prime factors of 348 are 2, 2, 3, 29

What is prime factorization of 348?

Prime factorization of 348 is 2 x 2 x 3 x 29 = 22 x 3 x 29.

Ariel has been assigned the task to find the product of all the prime factors of 348. Can you help her?

Prime factors of 348 are 2, 2, 3, 29.
Hence, the product of prime factors of 174.

Can you help Rubel to find out the product of the even factors of 348?

Factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348.
Even factors of 348 are 2, 4, 6, 12, 58, 116, 174, 348.
Hence, product of even factors of 348 is; 2 x 4 x 6 x 12 x 58 x 116 x 174 x 348 = 234658861056.