Factors that 84 are integers that deserve to be split evenly right into 84. That has total 12 determinants of i m sorry 84 is the best factor and also the prime factors of 84 are 2, 3 and 7. The element Factorization of 84 is 22 × 3 × 7.

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

What room the components of 84?

Factors of a given number room the numbers which divide the given number exactly 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 sized than the amount of its determinants (except 84).1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 = 140So, 84 is known as an numerous number.

How to calculation the components of 84?

Various methods such together prime factorization and the division method deserve to be used to calculate the components of 84. In prime factorization, we express 84 as a product of its element factors and in the division method, we watch what numbers divide 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 the 84 by prime Factorization

Prime factorization means expressing a number in terms of the product of its element factors. We have the right to do usage the division method or variable tree to execute this.

1. Prime Factorization by division method

The number 84 is separated by the smallest prime number which divides 84 exactly, i.e. It leaves a remainder 0. The quotient is then divided by the the smallest or second smallest prime number and the process continues it rotates the quotient becomes indivisible.

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

84 ÷ 2 = 42

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

42 ÷ 2 = 21

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

21 ÷ 3 =7

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

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

2. Prime Factorization by element Tree

The other way of prime factorization as taking 84 as the root, we develop branches by separating it by prime numbers. This method is comparable to above department method. The difference lies in presenting the factorization.The figure listed below shows the factor tree the 84. The composite number will have branches as they are further divisible. We continue making branches it spins we space left with only prime numbers.

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The numbers within the circles space the prime components of 84

Now that we have actually done the element factorization of our number, we can multiply them and also get the other factors. Can you shot and uncover out if every the factors are extended or not? and also as you could have currently guessed it, for prime numbers, there room no other factors.

Factors the 84 in Pairs

The aspect pairs that a number are the two numbers which, when multiplied, offer the compelled number.Considering the number 84, us have

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

So, the variable pairs the 84 are : (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12)

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

Important Notes:

Every number has a finite variety of factorsThe determinants of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84As 84 is strictly smaller than the amount of its determinants (leaving 84), the is dubbed an abundant number.

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

Solution:

To uncover the least number of boxes such that we deserve to cookies and brownies same in those boxes, we require to uncover the GCF (Gretest typical Factor) the 40 and 84

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

Common determinants of 40 and 84 = 1, 2, 4

So, GCF (40, 84) = 4

Hence, the least variety of boxes compelled is 4


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

Solution:

As we need to reduced both size garments into maximum equal width, we room going to find 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 the 90, 84 are 1, 2, 3, and 6. Out of these, 6 is greatest.Hence, she should consider to cut both the pieces right into a width of 6 inches.


 

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FAQs on components 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 unfavorable factors space -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.

What room the Prime factors of 84?

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

How countless Factors of 84 are likewise common to the determinants of 44?

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

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What is the amount of every the components of 84?

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

What is the Greatest typical Factor that 84 and 72?

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