Factors of 14: Factor tree, Division Method, Prime Factorization

In mathematics, factors of a number are the whole number ( take any number) that divides the given number evenly (into that number) with no remainder.  In the case of 14, the factors would be the numbers that can be divided by 14 without leaving a remainder. Factors of 14 are important in many mathematical calculations like simplifying fractions, finding common denominators and solving equations. Read further to learn more about the factors of 14, by division method, prime factorization, multiples, etc

What are the Factors of 14?

The factors of 14 are all positive integers that divide evenly into 14 without leaving a remainder, or they can be multiplied by two pairs of positive integers to get 14. There are four factors of 14: 1,2,7 and 14 itself. 

Let us understand in detail – 

• 1 divides into 14: 14 / 1 = 14 (with no remainder)
• 2 divides into 14: 14 / 2 = 7 (with no remainder)
• 7 divides into 14: 14 / 7 = 2 (with no remainder)
• 14 divides into 14: 14 / 14 = 1 (with no remainder) 

Note – It’s important to note that every number is a factor of itself.

Also Read – Factors of 20: Factor Tree, Division Method, Prime Factorization 

What is the Factor Tree for 14?

A factor tree is a visual representation of how a number can be broken down into its prime factors (factors that cannot be further divided into whole numbers). 

1. We know from previous discussions that 14 can be divided by 2 and 7 (without a remainder).
   
2. Since 2 is a prime number (itself and 1 is its only factor), we can leave it as is on the branch. However, 7 is also a prime number.
   
3. Since 7 is prime, there are no further factors to break it down into. So, the branch with 7 will simply end there.
   

Factors of 14 by Division Method

The division method is one of the simplest methods to find the factors of any number. In this method, we divide the number by smaller numbers starting from 1 and moving upwards to bigger numbers. If the division is exact, then the divisor is a factor. If we calculate it further, we find – 

• 14 ÷ 1 = 14 [Whole number]
• 14 ÷ 2 = 7 [Whole number]
• 14 ÷ 3 = 4.67 [Remainder in fraction]
• 14 ÷ 4 = 3.5 [Remainder in fraction]
• 14 ÷ 5 = 2.8 [Remainder in fraction]
• 14 ÷ 6 = 2.33.. [Remainder in fraction]
• 14 ÷ 7 = 2 [Whole number]

And if we divide 14 by the numbers 8, 9, 10 and further we will always get a remainder in fraction.

For example : 

• 14 ÷ 8 = 1.75  [Remainder in fraction]
• 14 ÷ 9 =1.556  [Remainder in fraction]
• 14 ÷ 10 = 1.4  [Remainder in fraction]
• 14 ÷ 11 = 1.273 [Remainder in fraction]
• 14 ÷ 12 = 1.167 [Remainder in fraction]
• 14 ÷ 13 = 1.077 [Remainder in fraction]
• 14 ÷ 14 = 1 [Remainder in fraction]
• 14 ÷ 15 =0.933 [Remainder in fraction]

Thus, the factors of 14 are 1, 2, 7, and 14.

Also Read – Factors of 12: Definition, Prime Factorization, Factor Tree

Factors of 14 by Multiplication Method

We have already seen the division method, let us know the factors of 14 through the Multiplication Method – 

• 1 × 14 = 14
• 2 × 7 = 14
• 7 × 2 = 14

Hence proved by the multiplication method. 

The factors are 1,2,7 and 14.

Factors of 14 by Prime Factorization

Prime factors are whole numbers greater than 1 that cannot be further broken down into whole numbers without a remainder. To find the prime factorization of 14, we can see the given steps – 

Step 1: When we divide 14 by the smallest prime factor, which is 2, we get – 14/2 = 7

Step 2: Further, when we divide 7  from the next prime factor that is itself 7. (Now, 2 and 3 are smaller than 7), we get – 7/7 = 1

Step 3: As we know, 1 cannot be divided by any other prime factor.

 Thus, what we get is –

14 = 2 x 7

Here, 2 and 7 are both prime numbers (numbers greater than 1 that can only be divided by 1 and themselves). So, 14 is built from these two prime factors.

Connecting to Factors:

While we do not do prime factorization of factors themselves, we can see how these prime factors are related to their actual factors:

• 1 (obtained by multiplying 1 x 1) – any number is a factor of itself by definition.
• 2 (obtained by multiplying 2 x 1) – as identified earlier.
• 7 (obtained by multiplying 1 x 7) – the other prime factor.
• 14 (obtained by multiplying 2 x 7) – the product of both prime factors.

Factor Pairs of 14

Factor pairs are like special partnerships among factors. Each pair, when multiplied, results in the original number (14). Here, let us take 14, now there are two types of factor pairs – 

Positive Factor Pair of 14

After multiplying two positive integers, the resulting value is known as the product, which is expressed in terms of a factor. Now let us pair the positive integers to get the number 14.

• 1 × 14 = 14
• 2 × 7 = 14
• 7 × 2 = 14
• 14 × 1 = 14

Negative Factor Pair of 14

After multiplying two negative integers, the resulting value is known as the product, which is expressed in terms of a factor. Now let us pair the negative integers to get the number 14.

• -1 × – 14 = 14
• -2 × -7 = 14
• -7 × -2 = 14
• -14 × -1 = 14

Thus, In the case of 14, we have two-factor pairs: (1, 14) and (2, 7).

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