Factors the 84 room integers that can be separated evenly right into 84. It has total 12 determinants of which 84 is the greatest factor and also the prime factors of 84 space 2, 3 and 7. The element Factorization the 84 is 22 × 3 × 7.

You are watching: What is the prime factorization of 84

Factors that 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and also 84Negative components of 84: -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42 and also -84Prime determinants of 84: 2, 3, 7Prime factorization of 84: 2 × 2 × 3 × 7 = 22 × 3 × 7Sum of determinants of 84: 224
 1 What space the components of 84? 2 How come Calculate factors of 84? 3 Factors the 84 by prime Factorization 4 Factors that 84 in Pairs 5 Important Notes 6 FAQs on factors of 84

## What are the factors of 84?

Factors that a given number room the number which division the provided number specifically without any remainder.Hence, the components of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.

84 is strictly smaller than the amount of its components (except 84).1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 = 140So, 84 is well-known as an numerous number.

## How to calculate the factors of 84?

Various methods such together prime factorization and also the department method have the right to be used to calculate the factors of 84. In element factorization, we express 84 as a product of its prime factors and also in the department method, we view what numbers division 84 exactly there is no a remainder.

Hence, the determinants of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and also 84.

Explore factors using illustrations and also interactive examples.

## Factors of 84 by prime Factorization

Prime factorization means expressing a number in regards to the product of its element factors. We can do use the division method or element tree to do this.

### 1. Prime Factorization by division method

The number 84 is separated by the smallest prime number i beg your pardon divides 84 exactly, i.e. It pipeline a remainder 0. The quotient is then separated by the the smallest or second smallest prime number and also the procedure continues it rotates the quotient becomes indivisible.

Since 84 is even, it will be divisible by 2.Let united state divide 84 by the element number 2

84 ÷ 2 = 42

42 is again even, let"s again divide by 2

42 ÷ 2 = 21

Now, 21 is one odd number. So the won"t be divisible through 2. Let"s examine the next prime number i.e. 3

21 ÷ 3 =7

7 is a element number. So, it"s not more divisible.

Prime administrate of 84 = 2 × 2 × 3 × 7

### 2. Element Factorization by variable Tree

The other means of prime factorization as taking 84 as the root, we produce branches by splitting it by prime numbers. This method is similar to above division method. The distinction lies in presenting the factorization.The figure listed below shows the aspect tree the 84. The composite number will have actually branches together they are more divisible. We proceed making branches till we room left with just prime numbers. The numbers within the circles are the prime determinants of 84

Now the we have actually done the element factorization of ours number, we deserve to multiply them and get the various other factors. Have the right to you try and uncover out if every the components are covered or not? and also as you might have already guessed it, for prime numbers, there room no other factors.

## Factors the 84 in Pairs

The aspect pairs the a number are the two numbers which, once multiplied, give the forced number.Considering the number 84, we have

1 × 84 = 84 2 × 42 = 84 3 × 28 = 84 4 × 21 = 84 6 × 14 = 84 7 × 12 = 84

So, the variable pairs that 84 are : (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12) The product of two an unfavorable numbers additionally results in a positive number i.e. (-ve) × (-ve) = (+ve).So, (-1, -84), (-2, -42), (-3, -28), (-4, -21), (-6, -14), (-7, -12). are additionally factor pairs of 84.Our emphasis in this write-up will it is in on the hopeful factors.

Important Notes:

Every number has actually a finite variety of factorsThe determinants of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and also 84As 84 is strictly smaller sized than the sum of its determinants (leaving 84), it is called an plentiful number.

Example 2: It"s time for a Christmas Party! Jennifer small 40 brownies and 84 cookies for her guests. She wants to fill them in box such the each box has actually equal variety of brownies and also cookies. What is the least variety of boxes she would need for this?

Solution:

To uncover the least number of boxes such the we have the right to cookies and brownies equally in those boxes, we need to uncover the GCF (Gretest common Factor) of 40 and 84

The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40The components of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and also 84

Common components of 40 and also 84 = 1, 2, 4

So, GCF (40, 84) = 4

Hence, the least number of boxes compelled is 4

Example 3: Julia has two pieces of cloth. The first one is 90 inches large and the 2nd one is 84 inches wide. She wants to reduced the two pieces right into equal width so that they are as wide as possible. What width should she consider for this?

Solution:

As we need to cut both size clothing into maximum same width, we space going to discover GCF (90,84)

The determinants of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90The determinants of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84

The common factors that 90, 84 are 1, 2, 3, and 6. The end of these, 6 is greatest.Hence, she should take into consideration to cut both the pieces right into a broad of 6 inches. ## FAQs on determinants of 84

### What are the factors of 84?

The factors of 84 space 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and also its an adverse factors are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.

### What are the Prime components of 84?

The prime determinants of 84 are 2, 3, 7.

### How numerous Factors of 84 are also common come the components of 44?

Since, the components of 84 space 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and the components of 44 space 1, 2, 4, 11, 22, 44.Hence, <1, 2, 4> room the usual factors the 84 and also 44.

See more: How Many Ounces Is 85 G To Oz, How Many Ounces Are In 85 Grams

### What is the amount of all the components of 84?

Sum the all factors of 84 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) = 224

### What is the Greatest common Factor that 84 and 72?

The determinants of 84 and 72 room 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively.Common determinants of 84 and 72 are <1, 2, 3, 4, 6, 12>.Hence, the Greatest typical Factor that 84 and 72 is 12.