Factors of 14 | Prime Factorization of 14 - Explained Simply

Today we are going to present here Factor Tree of 14. The factor is the number that divides the original number. The factors of 14 are 1, 2, 7 and 14 itself.

What are the factors of 14?

We want to find all the whole numbers that can divide 14 without leaving any remainder.

Factor Tree Method of 14: Explained Simply

To find all the factors of 14, we can systematically test numbers, starting from 1 and see which ones divide 14 evenly.

Start with 1:

1 is a factor of every number.

14 ÷ 1 = 14

This gives us our first pair of factors: (1, 14)

Step 2:

Is 14 divisible by 2? Yes, because 14 is an even number.

14 ÷ 2 = 7

This gives us our second pair of factors: (2, 7)

Step 3:

Is 14 divisible by 3? If you divide 14 by 3, you get 4 with a remainder of 2 (3 x 4 = 12).

So, 3 is NOT a factor of 14.

Step 4:

Is 14 divisible by 4? If you divide 14 by 4, you get 3 with a remainder of 2 (4 x 3 = 12).

So, 4 is NOT a factor of 14.

Step 5:

Numbers divisible by 5 must end in 0 or 5. 14 ends in 4.

So, 5 is NOT a factor of 14.

Step 6:

Is 14 divisible by 6? If you divide 14 by 6, you get 2 with a remainder of 2 (6 x 2 = 12).

So, 6 is NOT a factor of 14.

Finally, Step 7:

We've already found 7 when we paired it with 2 (2 x 7 = 14).

Once you reach a number that you've already found as part of a pair (or if you reach the square root of the number), you've found all the unique factors.

So, we stop here.

The Factors of 14

Based on our systematic check, the factors of 14 are 1, 2, 7 and 14.

Prime Factorization of 14

There are two primary methods commonly used to find the prime factorization of a number:

Division Method: Repeatedly dividing the number by prime numbers until the quotient is also a prime number.

Factor Tree Method: Breaking down the number into any two factors, and then continuing to break down non-prime factors until all branches end in prime numbers.

Let's apply both methods to our target number 14.

Prime Factorization of 14 using the Division Method

The division method involves systematically dividing the number by the smallest possible prime numbers until you can no longer divide it further.

Steps:

Start with the number 14. We want to find its prime factors.

Find the smallest prime number that divides 14 evenly.

The smallest prime number is 2.

Does 2 divide 14 evenly?

Yes, 14 ÷ 2 = 7.

Note the result (7) and the prime divisor (2).

Our current prime factor is 2.

Our remaining number to factor is 7.

Check if the remaining number (7) is a prime number.

Yes, 7 is a prime number (its only factors are 1 and 7).

Stop. Since the remaining number is prime, we have found all the prime factors.

Result: The prime factors are the prime divisors used and the final prime number.

So, the prime factors of 14 are 2 and 7.

We can write this as a multiplication: 14 = 2 × 7

Prime Factorization of 14 using the Factor Tree Method

The factor tree method provides a visual way to break down a number into its prime factors.

Steps:

Start with the number 14 at the top of your "tree."

/ \

1 14

Find any two factors of 14 (other than 1 and 14).

The most straightforward pair is 2 and 7.

/ \

② ⑦

Check if these factors are prime numbers.

Is 2 a prime number?

Yes. Circle it to show it's a prime factor.

Is 7 a prime number?

Yes. Circle it to show it's a prime factor.

Stop. Since all the "branches" of your tree end in prime numbers, you have completed the factorization.

Result: The circled numbers at the end of the branches are the prime factors.

So, the prime factors of 14 are 2 and 7.

We can write this as a multiplication: 14 = 2 × 7

Both methods yield the same result,

confirming that the prime factorization of 14 is 2 × 7.