Factors of 84 room integers that can be split evenly right into 84. It has full 12 determinants of i m sorry 84 is the biggest factor and the prime factors of 84 space 2, 3 and also 7. The element Factorization the 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 factors of 84: -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42 and -84Prime components of 84: 2, 3, 7Prime factorization of 84: 2 × 2 × 3 × 7 = 22 × 3 × 7Sum of components of 84: 224
1.What room the determinants of 84?
2.How come Calculate factors of 84?
3.Factors that 84 by prime Factorization
4.Factors that 84 in Pairs
5.Important Notes
6.FAQs on factors of 84

What space the factors of 84?

Factors of a given number room the number which divide the given number exactly without any type of remainder.Hence, the components of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and also 84.

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

How to calculate the factors 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 prime factors and in the department method, we see what numbers divide 84 exactly there is no a remainder.

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

Explore components using illustrations and interactive examples.

Factors the 84 by prime Factorization

Prime factorization way expressing a number in regards to the product the its element factors. We deserve to do usage the department method or element tree to carry out this.

1. Element Factorization by department method

The number 84 is separated by the smallest prime number i beg your pardon divides 84 exactly, i.e. It leaves a remainder 0. The quotient is then split by the the smallest or 2nd smallest element number and the procedure continues it rotates the quotient i do not care indivisible.

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

84 ÷ 2 = 42

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

42 ÷ 2 = 21

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

21 ÷ 3 =7

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

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

2. Element Factorization by aspect Tree

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

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The numbers inside the circles space the prime determinants of 84

Now the we have 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 can have currently guessed it, because that prime numbers, there room no various other factors.

Factors that 84 in Pairs

The aspect pairs that a number are the 2 numbers which, as soon as multiplied, provide the forced 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 element pairs the 84 are : (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12)

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

Important Notes:

Every number has a finite number of factorsThe factors 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 components (leaving 84), the is dubbed an numerous number.

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

Solution:

To find the least number of boxes such that we can cookies and also brownies equally in those boxes, we require to discover the GCF (Gretest usual Factor) the 40 and also 84

The determinants 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 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 large and the second one is 84 inch wide. She desires to cut the two pieces into equal width so the they are as wide as possible. What width have to she consider for this?

Solution:

As we require to reduced both size clothes into maximum equal width, we room going to discover GCF (90,84)

The determinants of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and also 90The components 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 also 6. The end of these, 6 is greatest.Hence, she should take into consideration to reduced both the pieces right into a width of 6 inches.


 

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FAQs on components of 84

What room the determinants of 84?

The determinants of 84 space 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and its negative factors room -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.

What room the Prime components of 84?

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

How numerous Factors that 84 are also common to the determinants of 44?

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

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What is the amount of all the factors of 84?

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

What is the Greatest usual Factor of 84 and 72?

The factors of 84 and 72 space 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 also 72 are <1, 2, 3, 4, 6, 12>.Hence, the Greatest common Factor of 84 and 72 is 12.