In this lesson, you’ll learn what the factors of 14 are, and how to work them out.
A factor is a number that multiplies into another number exactly, without leaving a remainder.
For example, 2 and 7 multiply together to make 14 so, they are two of 14’s factors.
Once you know how to work out the factors of a number, you’ll be able to easily find the factors of any number!
All Factors of 14
The factors of 14 are: 1, 2, 7, 14.
You can write 14 in terms of its pairs of factors or its prime decomposition, we’re going to take a look at each of those methods and how to work them out.
Factor Pairs of 14
Factor pairs are two whole numbers which when multiplied together give a certain number.
The factor pairs of 14 are:
Each number in a factor pair is a factor. Factors can also be known as divisors because they divide a number without leaving a remainder.
When you multiply two negative numbers together, you get a positive number, so negative numbers can also be factors:
A prime number is one that can only be divided by itself, or 1. For example, 5 can only be divided by 5, or 1 so it is a prime number.
A prime factor is a factor, which is also prime!
14 has 2 prime factors:
Notice 1 is not a prime factor as it only has the divisor 1.
How to Find the Factors of 14
To find every factor, you need to check whether 14 can be divided by each whole number starting with 1.
When dividing 14 by a number, if the result is a whole number without a remainder, the divisor and the result are both factors.
This is how we make factor pairs!
Start by dividing by 1…
Both 1 and 14 are factors. This can be written as the factor pair (1, 14)
The result has no remainder, so 2 and 14 are both factors of 14. They can be written as a factor pair, (2,14).
The result is not a whole number, so 3 is not a factor of 14!
You can stop when you reach the square root of 14, which is 3.74….
So you don’t need to check 4.
However, there are also negative factor pairs. The negative of every factor pair is also another factor pair of 14.
14 has the factors: 1, 2, 7, 14, -1, -2, -7, -14.
It is a small number so it doesn’t take long to check whether certain numbers go into 14.
When you find the factors of larger number, here is a table with tricks for spotting factors from 1 to 10:
Trick to spot the factor
|Every integer has a factor of 1.|
|You can spot a factor of 2 if the number is even.|
|A number has a factor of 3 if the sum of its digits is a multiple of 3.|
|There is a factor of 4 in numbers whose last two digits are 00 or a multiple of 4.|
|You can spot a factor of 5 if the last digit is 0 or 5.|
|A number has a factor of 6, it is even and the sum of its digits are a multiple of 3|
|The trick to spotting a factor of 7 is more complex than the others!|
|To spot a factor of 8, divide it by 2 and check for divisibility by 4.|
|A number has a factor of 9 if its digits are divisible by 9.|
|You can spot factors of 10 in numbers ending in 0.|
Using the test above, see if you can find the factors of 144!
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Prime Factorization of 14
Prime factorization involves writing a number as the product of its prime factors.
There are a couple of different ways to find the prime factorization of a number.
The easiest way is to use a factor tree.
Method 1: Factor Tree
A number can be broken down into pairs which are shown as separate branches on the tree.
These branches can then be broken down further into pairs. When there is a prime at the end of every branch, the tree is complete.
Starting with 14 at the top of the tree, this can be broken down into the factor pair (2, 7).
2 and 7 are both prime factors so both can be circled to show both branches are complete.
As the end of both branches are prime and circled, the tree is finished.
14 can be written as a product of every circled branch.
Method 2: Dividing
An alternative way to find the prime decomposition of 14, is to keep breaking down the factors until you reach 1.
Look at the factors of 14 and choose the smallest of its prime factors. Divide 114 by this number, then continue dividing the result by this prime factor.
If the result has a remainder, don’t include this as a factor in the product and move on to the next smallest prime factor.
Continue doing this until the result is 1. This is when all factors in the product have been found.
The factors which are prime numbers are 2 and 7, so 14 can be broken down into its prime factors using 2 and 7.
Start with 2, as it is the smallest prime factor…
7 is a whole number, so 2 is included in the product. Carry on dividing by 2…
The result is not an integer, so 2 is included once in the product.
Moving on to the next prime factor in increasing order…
The result is not an integer, and neither is dividing by the next greatest prime, 5.
The next prime after 5 is 7, so 7 is the last number in the prime factorization.
1 is not included in the product because 1 isn’t prime.
Writing 14 as a product of the factors found…
a) Find the prime factorization of 66.
b) Find the prime factorization of 34.
a) 66 = 2 × 3 × 11
b) 34 = 22 × 32
Isn’t 14 interesting?
A period of 14 days is half of the Moon’s cycle. It takes 14 days for the Moon to change from a new to a full moon.
The atomic number of silicon is 14.
14 is the approximate weight of nitrogen.
There are 14 lines in a sonnet, a type of poetic form.
A woodlouse has a total of 14 legs.
A golf player can have no more than 14 golf clubs in their bag.
And finally, 14 is the number of muscles used to smile!
To Sum Up (Pun Intended!)
A factor is an integer that divides exactly into another, where the result has no remainder.
Factor pairs are two numbers that multiply together to give a certain product and are expressed in brackets, for example (1, 14).
The factors of 14 are:
The factors of a number also include negative factors as the product of two negative numbers is positive.
To find all of 14’s factors, check if each whole number from 1 to the square root of 14, can be divided into 14 without a remainder.
Leave a comment below if you have any questions and let us know how you did in the challenges!