A element is a Latin word, and also it method "a doer" or "a maker" or "a performer." A factor of a number in math is a number that divides the given number. Hence, a aspect is nothing however a divisor the the provided number. To uncover the factors, we have the right to use the multiplication and also the department method. We can likewise apply the divisibility rules.

You are watching: A number which divides evenly into a given number is called a ___ of that number.

Factoring is a helpful skill to discover factors, i beg your pardon is more utilized, in real-life situations, such as dividing something into equal components or splitting in rows and also columns, comparing prices, exchanging money and also understanding time, and making calculations, during travel.

1.What room Factors?
2.Properties the Factors
3.How to uncover the determinants of a Number?
4. Finding the number of Factors
5.Algebra Factors
6.FAQs ~ above Fractions

What are Factors?


In math, a aspect is a number that divides another number evenly, that is with no remainder. Components can be algebraic expressions as well, dividing one more expression evenly. Well, factors and also multiples are a component of our everyday life, native arranging things, such together sweets in a box, taking care of money, to finding fads in numbers, resolving ratios, and working with expanding or reducing fractions.

Factor an interpretation

A factor is a number the divides the offered number without any remainder. Components of a number deserve to be referred to as number or algebraic expressions the evenly divide a given number/expression. The determinants of a number can either be confident or negative.

For example, let's check for the factors of 8. Since 8 can be factorized as 1 × 8 and 2 × 4 and also we know that the product that two negative numbers is a hopeful number only. Therefore, the components are 8 space actually 1, -1, 2, -2, 4, -4, 8 and also -8. Yet when it involves problems regarded the factors, only positive numbers space considered, that also a totality number and also a non-fractional number.


Properties that Factors


Factors of a number have actually a certain number of properties. Given below are the properties of factors:

The variety of factors of a number is finite.A aspect of a number is always less than or equal to the provided number.Every number except 0 and 1 contends least 2 factors, 1 and itself.

How to Find components of a Number?


We can use both "Division" and "Multiplication" to find the factors.

Factors by Division

To uncover the factors of a number making use of division:

Find every the numbers much less than or same to the provided number.Divide the provided number by every of the numbers.The divisors that give the remainder to be 0 room the components of the number.

Example: find the positive determinants of 6 making use of division.

Solution:

The positive numbers that are much less than or same to 6 room 1, 2, 3, 4, 5, and also 6. Let us divide 6 by each of this numbers.

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We have the right to observe that divisors 1, 2, 3, and, 6 offer zero together the remainder. Thus, components of 6 room 1, 2, 3, and 6.

Factors by Multiplication

To discover the determinants using the multiplication:

Write the offered number as the product of two numbers in different possible ways.

All the numbers the are affiliated in every these assets are the factors of the provided number.

Example: uncover the positive factors of 24 making use of multiplication.

Solution:

We will write 24 together the product of two numbers in lot of ways.

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All the numbers that are connected in these commodities are the components of the provided number (by the definition of a element of a number)

Thus, the components of 24 room 1, 2, 3, 4, 6, 8, 12, and 24.


Finding the number of Factors


We can discover the number of factors of a provided number using the complying with steps.

Step 3: write the prime factorization in the exponent form.Step 3: include 1 to every of the exponents.Step 4: Multiply all the resultant numbers. This product would offer the number of factors that the provided number.

Example: find the number of factors of the number 108.

Solution:

Perform prime administer of the number 108:

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Thus, 108 = 2 × 2 × 3 × 3 × 3. In the exponent form: 108 = 22 × 33. Add 1 to every of the exponents, 2 and also 3, here. Then, 2 + 1 = 3, 3 + 1 = 4. Multiply these numbers: 3 × 4 = 12. Thus, variety of factors that 108 is 12.

The actual factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and also 108. Here, 108 has 12 factors and hence our above answer is correct.


Algebra-Factors


Factors do exist because that an algebraic expression as well. For example, the determinants of 6x room 1, 2, 3, 6, x, 2x, 3x, and 6x. There room different types of steps to find components in algebra. Some of them room as follows:

We will learn around these species of factoring in higher grades. Click on the above links to learn each of lock in detail.

Factors of Numbers

Given below is the list of subject that room closely associated to Factors. This topics will likewise give friend a glimpse of how such principles are extended in altoalsimce.org.

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Example 2: which of the following statement(s) is/are true?

The element of a number can be higher than the number.

Some numbers can have one infinite number of factors.

Solution:

1. The statement, "The element of a number deserve to be greater than the number," is FALSE. We understand that components are the divisors of the number that leave 0 as the remainder. Hence, castle are constantly less 보다 the number. Therefore, the price is: False

2. The statement, "Some numbers have the right to have an infinite number of factors," is FALSE. The variety of factors that a number is finite. Therefore, the prize is: False.


Example 3: discover the number of factors of 1620.

Solution:

To find the prime factorization that 1620 we will certainly follow the factor tree methodology here.

See more: Atlanta To Birmingham Distance From Atlanta To Birmingham Alabama )

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Thus, 1620 = 22 × 34 × 51. Addinng 1 to every of the exponents, us get: 2 + 1 = 3, 4 + 1 = 5,1 + 1 = 2. The product of all these numbers: 3 × 5 × 2 = 30. Therefore, the variety of factors of 1620 is 30.