# Factors of 294

Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294

#### How to find factors of a number

 1.   Find factors of 294 using Division Method 2.   Find factors of 294 using Prime Factorization 3.   Find factors of 294 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 294

• Divide 294 by 1: 294 ÷ 1 : Remainder = 0
• Divide 294 by 2: 294 ÷ 2 : Remainder = 0
• Divide 294 by 3: 294 ÷ 3 : Remainder = 0
• Divide 294 by 6: 294 ÷ 6 : Remainder = 0
• Divide 294 by 7: 294 ÷ 7 : Remainder = 0
• Divide 294 by 14: 294 ÷ 14 : Remainder = 0
• Divide 294 by 21: 294 ÷ 21 : Remainder = 0
• Divide 294 by 42: 294 ÷ 42 : Remainder = 0
• Divide 294 by 49: 294 ÷ 49 : Remainder = 0
• Divide 294 by 98: 294 ÷ 98 : Remainder = 0
• Divide 294 by 147: 294 ÷ 147 : Remainder = 0
• Divide 294 by 294: 294 ÷ 294 : Remainder = 0

Hence, Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, and 294

#### 2. Steps to find factors of 294 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 294 using the division method, follow these steps:

• Step 1. Start dividing 294 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 294, which is 2. Divide 294 by 2 to obtain the quotient (147).
294 ÷ 2 = 147
• Step 3. Repeat step 1 with the obtained quotient (147).
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 294 is, 294 = 2 x 3 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 294 as shown below:

So, the prime factorization of 294 is, 294 = 2 x 3 x 7 x 7.

#### 3. Find factors of 294 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 294 would be the two numbers which, when multiplied, give 294 as the result.

The following table represents the calculation of factors of 294 in pairs:

Factor Pair Pair Factorization
1 and 294 1 x 294 = 294
2 and 147 2 x 147 = 294
3 and 98 3 x 98 = 294
6 and 49 6 x 49 = 294
7 and 42 7 x 42 = 294
14 and 21 14 x 21 = 294

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 294. They are called negative pair factors.

Hence, the negative pairs of 294 would be ( -1 , -294 ) , ( -2 , -147 ) , ( -3 , -98 ) , ( -6 , -49 ) , ( -7 , -42 ) and ( -14 , -21 ) .

#### 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. 294 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, 7, 14, 21, 42, 49, 98, 147, 294 are exact divisors of 294.
• 1 is a factor of every number. Eg. 1 is a factor of 294.
• Every number is a factor of zero (0), since 294 x 0 = 0.

• How do you find factors of a negative number? ( eg. -294 )?

Factors of -294 are -1, -2, -3, -6, -7, -14, -21, -42, -49, -98, -147, -294.

• What is the sum of all factors of 294?

The sum of all factors of 294 is 684.

• What is prime factorization of 294?

Prime factorization of 294 is 2 x 3 x 7 x 7.

• What are the pair factors of 294?

Pair factors of 294 are (1,294), (2,147), (3,98), (6,49), (7,42), (14,21).

• What are six multiples of 294?

First five multiples of 294 are 588, 882, 1176, 1470, 1764, 2058.

• Is 294 a whole number?

Yes 294 is a whole number.

• Which is the smallest prime factor of 294?

Smallest prime factor of 294 is 2.

• What are five multiples of 294?

First five multiples of 294 are 588, 882, 1176, 1470, 1764.

• Write all factors of 294?

Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294.

#### Examples of Factors

Joey wants to write all the prime factors of 294 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 294 are 2, 3, 7, 7.
So in exponential form it can be written as 2 x 3 x 72.

How many factors are there for 294?

Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 294. Can you predict the answer?

11 factor(s) of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147.

Sammy is puzzled while calculating the prime factors of 294. Can you help him find them?

Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294.
Prime factors of 294 are 2, 3, 7, 7

What is prime factorization of 294?

Prime factorization of 294 is 2 x 3 x 7 x 7 = 2 x 3 x 72.

Ariel has been assigned the task to find the product of all the prime factors of 294. Can you help her?

Prime factors of 294 are 2, 3, 7, 7.
Hence, the product of prime factors of 42.

Can you help Rubel to find out the product of the even factors of 294?

Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294.
Even factors of 294 are 2, 6, 14, 42, 98, 294.
Hence, product of even factors of 294 is; 2 x 6 x 14 x 42 x 98 x 294 = 203297472.