Factors of 14—with division and prime factorization

Factors of 14

Factors of 14

Factors of 14 are those real numbers that can divide an original number evenly with no remainder. 

For example:

2 is the factor of 14 since when we divide 14 by 2, we get a whole number, such as;

14 divided by 2 ⇒ 14 ÷ 2 = 7

In this article, we can also find the other factors of 14. In addition, we will meet the pair factors of 14, that produce the original number when multiplied together. The prime factors of a number are the prime numbers that can evenly divide the original number.

Factors of 14

 

What are Factors of -14?

When we multiply two numbers, and we get -14 as a product, that numbers are the factors of -14. 

Here is the explanation:

-1 × 14 = -14

 1 × -14 = -14

 -2 × 7 = -14

 2 × -7 = -14

We can get -14 by having (-1, 14), and(-2, 7) as a pair of factors. Similarly, we can also get -14 by having(-1, 14), and(-2, 7) as a pair of factors.

How to Find Factors of 14?

Those factors of 14 that can divide an original number without leaving any remainder are called factors of 14. As we divide 14 by the smallest natural number, we continue dividing it by 14.

14 ÷ 1 = 14 [Whole number]

14 ÷ 2 = 7 [Whole number]

14 ÷ 3 = 4.67 [Fraction]

14 ÷ 4 = 3.5 [Fraction]

14 ÷ 5 = 2.8 [Fraction]

14 ÷ 6 = 2.33.. [Fraction]

14 ÷ 7 = 2 [Whole number]

We can divide 14 even further by 8, 9, 10, 11, 12, and 13, and we will get only a fraction.

In the end, divide 14 by itself to get a quotient equal to 1.

14 ÷ 14 = 1 [Whole number]

Therefore, the factors of 14 include only 1, 2, 7, and 14.

More Factors

Factors of 21= 1, 3, 7, 21.

Factors of 12= 1, 2, 3, 4, 6, and 12.

Factors of 18=  1, 2, 3, 6, 9, and 18.

Factors of 24= 1, 2, 3, 4, 6, 8, 12, and 24.

Factors of 81= 1, 3, 9, 27, and 81.

Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42.

Pair Factors of 14

Multiply the two numbers to find the pair factor of 14, and you will get the original number as 14.

1 × 14 = 14

2 × 7 = 14

As a result, the pair factors are (1, 14) and (2, 7). They are positive pair factors.

Similarly, negative pair factors can also be considered. If we multiply two negative factors, we will get a positive result.

-1 × -14 = 14

-2 × -7 = 14

Thus, the negative pair factors are (-1, -14) and (-2, -7).

Prime Factorization of 14

We can find the prime factors of 14 by dividing it by each prime number, until we get 1.

Factors of 14 by prime factorization

Step 1: Take 14 and divide it by the smallest prime factor, which is 2.

14/2 = 7

Step 2:

Dividing 7 by its own prime factor, 7 itself, (Since 2 and 3 are smaller than 7).

7/7 = 1

Step 3: 

Further, we cannot divide 1 by any prime factor. Thus,

Prime factorization of 14 = 2 x 7

Solved Examples

Q.1: If there are 14 oranges to be distributed among 7 members in a room. How many oranges does each member get?

Solution: 

Given,

Number of oranges = 14

Number of members in room = 7

Each member will get = 14/7 = 2 oranges

Q.2: Calculate the sum of all the factors of 14?

Solution: 

The factors of fourteen are 1, 2,7 and 14.

Sum = 1 + 2 + 7 + 14 = 24

Thus, 24 is the required sum.

Q.3: What are the common factors of 7 and 14?

Solution: 

The factors of each number must be written down in order to find the common factors.

7 is a prime number, it has only two factors.

7 = 1 and 7

Since 14 is a composite number, it has more than two factors.

14 = 1, 2, 7 and 14

Therefore, the common factors among 7 and 14 are 1 and 7.

Factors of 13

Factors of 84

FAQ’s

What are the total factors of 14?

The factors of 14 are 1, 2, 7, and 14. Thus, in total there are four factors.

14 is a multiple as well as a factor of 14. True or false?

It is true. Natural number 14 is both a factor of and a multiple of because 14 divided by 14 equals 1 and 14 multiplied by 1 equals 14.

What are the multiples of 14?

The first 10 multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126 and 140.

What are the prime factors of 14?

14 has a prime factorization of 2 × 7. Thus, the prime factors are 2 and 7.

What is the average of factors of 14?

The average is the sum of all the factors divided by the number of factors.

Average (factors of 14) = (1+2+7+14)/4 = 24/4 = 6

Thus, the required average is 6.

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