What is the prime factor of 84

Write the numbers from 1 to 12 in both the first column and the top row so that this puzzle functions like a multiplication table.

Table of Contents Show

Factors of 84:
Sum-Difference Puzzle:
More about the Number 84:
Answer to This Week’s Puzzle:
Prime Factorization of 84
Prime Factorization of 84 by Upside-Down Division Method
Prime Factorization of 84 by Factor Tree Method

This week’s puzzles and last week’s solutions: 12 Factors 2014-04-07

Factors of 84:

84 is a composite number. 84 = 1 x 84, 2 x 42, 3 x 28, 4 x 21, 6 x 14, or 7 x 12. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Prime factorization: 84 = 2 x 2 x 3 x 7 which can also be written 2² x 3 x 7.

Sometimes 84 is a clue in the FIND THE FACTORS 1 – 12 puzzles. Even though it has other factors, we only use 84 = 7 x 12 in the puzzles.

Sum-Difference Puzzle:

84 has six factor pairs. One of those factor pairs adds up to 25, and another one subtracts to 25. If you can identify those factor pairs, then you can solve this puzzle!

More about the Number 84:

84 is prominent in this cool pattern:

Answer to This Week’s Puzzle:

Here we have a collection of all the information you may need about the Prime Factors of 84. We will give you the definition of Prime Factors of 84, show you how to find the Prime Factors of 84 (Prime Factorization of 84) by creating a Prime Factor Tree of 84, tell you how many Prime Factors of 84 there are, and we will show you the Product of Prime Factors of 84.

Prime Factors of 84 definition

First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of 84 are all the prime numbers that when multiplied together equal 84.
How to find the Prime Factors of 84 The process of finding the Prime Factors of 84 is called Prime Factorization of 84. To get the Prime Factors of 84, you divide 84 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1. This Prime Factorization process creates what we call the Prime Factor Tree of 84. See illustration below.

All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 84. Here is the math to illustrate: 84 ÷ 2 = 4242 ÷ 2 = 2121 ÷ 3 = 77 ÷ 7 = 1 Again, all the prime numbers you used to divide above are the Prime Factors of 84. Thus, the Prime Factors of 84 are: 2, 2, 3, 7.
How many Prime Factors of 84? When we count the number of prime numbers above, we find that 84 has a total of 4 Prime Factors.

Product of Prime Factors of 84

The Prime Factors of 84 are unique to 84. When you multiply all the Prime Factors of 84 together it will result in 84. This is called the Product of Prime Factors of 84. The Product of Prime Factors of 84 is: 2 × 2 × 3 × 7 = 84

Prime Factor Calculator

Do you need the Prime Factors for a particular number? You can submit a number below to find the Prime Factors of that number with detailed explanations like we did with Prime Factors of 84 above.

Prime Factors of 85

We hope this step-by-step tutorial to teach you about Prime Factors of 84 was helpful. Do you want a test? If so, try to find the Prime Factors of the next number on our list and then check your answer here. Copyright | Privacy Policy | Disclaimer | Contact

Factors of 84 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 84 with a remainder of zero, then that number is called a factor.

All Factors: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Prime Factors: 2, 3, 7
Factors in pairs: (1,84),(2,42),(3,28),(4,21),(6,14),(7,12)

Now, let us see the prime factors and prime factorization of the number.

Prime Factorization of 84

Prime factorization is a method of “expressing” or finding the given number as the product of prime numbers. If a number occurs more than once in prime factorization, it is usually expressed in exponential form to make it more compact.

The prime factorization comes out to be: 2 x 2 x 3 x 7

Prime Factorization of 84 by Upside-Down Division Method

Upside-Down Division is one of the techniques used in the Prime factorization method to find factors of numbers.

In this method, you will divide a given “composite” number evenly by the several prime numbers(starting from the smallest) till it gets a prime number.

It is called Upside-Down Division because the symbol is flipped upside down.

Here, 84 is an even number. So it is undoubtedly divisible by 2 with no remainder.

Thus we do 84÷ 2 = 42. Now find the prime factors of the obtained quotient.

Repeat Step 1 and Step 2 until we get a result of prime number as the quotient. Here, 42 is the quotient. Now find the prime factor of 42

42÷ 2 = 21

Similarly 21÷ 7 = 3. Here, 3 is the prime number.

So we can stop the process.

So, now the prime factorization of 84 with the upside-down division method is 2 × 2 × 3 × 7.

Prime Factorization of 84 by Factor Tree Method

The Factor tree method is another technique for producing the prime factorization and all factors of a given number.

To use this method for a number x,

Firstly consider two factors say a,b of x such that a*b is equal to x and at least one of them (a, b) is a prime factor say a.

Then consider two factors of b say c, d such that again at least one of them is a prime factor. This process is repeated until both the factors are prime i.e if we get both the factors as prime at any step, we stop the process there.

Following is the factor tree of the given number.

Here we can get the prime factorisation of 84 as 2 * 2 * 3 * 7 and the prime factors are 2, 3 and 7