Factors Of 6 In Pairs

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Factors are the numbers that are multiplied together to obtain a production.

For example: The product of half-dozen × 7 = 42. It means that the numbers half-dozen and 7 are factors of 42.

What are Cistron Pairs?

In math, a factor pair is defined as a gear up of ii factors, which, when multiplied together, give a particular product. In other words, it is a set of two numbers nosotros multiply to become a product.

For example, in the multiplication argument, six × 7 = 42, half-dozen and 7 is one of the factor pair that gives united states of america the production 42.

In other words, 42 is the product of 6 and vii.

A number tin can take multiple gene pairs. We can write the factor pair as (a, b) where a and b are the factors of the number.

For instance: For the number 24;

Factors of 24 are 1, 2, 3, 4, half-dozen, 8, 12 and 24

We tin write 24 as the product of 1 × 24; 2 × 12 ; 3 × 8; 4 × 6

Then, the cistron pairs of 24 are (1, 24); (2, 12); (3, eight) and (4, half dozen).

Cistron Pairs of Integers

An integer is a whole number(not in fractional grade) that tin be positive, negative or 0.

For example: -iii, -10, 0, 18 etc.

Positive Integers

Gene pairs of positive integers are the pairs of integers whose product will be the integer.

For instance: Factors of 12 are 1, ii, 3, 4, 6, and 12.

Nosotros tin write 12 = 1 × 12; 2 × 6; 3 × four

So, the cistron of 12 in pairs = (i, 12); (2, 6); (3, iv)

Negative Integers

Negative numbers are the numbers that lie on the left side of 0. For case: -2, -10, -150.

When nosotros talk about the factor pairs of such numbers, nosotros need to see the sign of the number. Since, the negative numbers take minus(-) sign in front of them, so one factor in the factor pair volition be a negative number.

For example: Find the factor pairs of -24.

Factors of -24 are 1, ii, 3, 4, vi, 8, 12, 24, -1, -ii, -three, -4, -six, -viii, -12, and -24.

We can write -24 = one × -24, ii × -12, 3 × -viii, 4 × -6, 6 × -4, 8 × -three, 12 × -2, and 24 × -1.

The gene pairs of -24 are (1, -24); (2, -12); (3, -viii); (four, -6); (vi, -4); (8, -3); (12, -2); (24, -i).

Prime Numbers

Prime number is a number that has simply two factors, 1 and the number itself.

Any prime number number volition accept only a single cistron pair since there are only two factors. For Example: For the prime number 13: 13 × 1 = 13, therefore it has just ane factor pair. In this instance the cistron pair will be (ane, 13) only.

Factor Pairs of Fractions

Fractions are the numbers that can be represented in the grade of $\frac{p}{q}$ where p is the numerator and q is the denominator. For instance: $\frac{three}{five}$, $\frac{11}{15}$ etc.

Finding the factors of the fractions is the same as finding the factors of a whole number.

For example: In the fraction $\frac{three}{5}$, factors of 3 are i, iii and factors of 5 are 1, v.

Then, the factors of $\frac{3}{5}$ are i, iii,$ \frac{1}{v}$, $\frac{3}{v}$.

And so, the cistron pairs of $\frac{three}{5}$ are (1, $\frac{three}{5})$; (3, $\frac{i}{five}$).

Factor Pairs of Decimal Number

A decimal number is a number whose whole number part and the fractional function is separated by a decimal bespeak. For instance: 1.ii, 3.456, 5.28 etc

For case: For the decimal 1.2.

Factors of i.two are 1, 2, 3, 4, half dozen, 12, 0.1, 0.2, 0.3, 0.4, 0.vi, 1.2.

The gene pairs of 1.ii are (1, i.2); (2, 0.6); (3, 0.4); (four, 0.3); (6, 0.2); (12, 0.1).

Factor Pairs of Algebraic Expressions

An algebraic expression is an expression that is fabricated up of variables and constants along with the algebraic operations like addition, subtraction etc.

The factors of an algebraic expression can be formed by either splitting the middle term or finding the HCF.

Instance i: For the expression two x + half-dozen

two x + six = ii (x + three)

Factors of ii x + 6 are 1, ii, (x + 3), (2 10 + six).

And so, the factor pairs of 2 ten + 6 are (one, (2 x + vi)) and (2, (x + 3)).

Example 2: For the expression $x^ 2$ – 10-2.

$10^2$ – x – ii = $x^2$ – two x + x – 2 = ten (x – ii) + 1(x – 2) = (x + 1) (ten – 2)

Factors of $x^ 2$ – x – two are one, (10 + 1), (x – 2) and ($10^2$ – x – 2)

Then, the factor pairs of $x^two$ – x – ii are (1, ($x^2$ – ten – 2)); ((ten + i),(x – 2)).

Conclusion

In this article, we learnt about factor pairs. The pair of two factors which gives the product is known as factor pair. To read more than such informative articles on other concepts, exercise visit our website. We, at SplashLearn, are on a mission to make learning fun and interactive for all students.

Solved Examples

ane. Find the gene pairs of the whole number 25?

Respond: The factors of 25 are 1, v and 25.

The factor pairs of 25 are (one, 25) and (5, 5).

2. How many cistron pairs can you find for the number 35?

Respond: Factors of 35 are ane, 5, 7 and 35.

The cistron pairs of 35 are (1, 35) and (5, 7).

So, there are ii factor pairs for the number 35.

3. What are the gene pairs of two.45?

Answer: The factors of 2.45 are i, v, seven, 0.1, 0.five, 0.7, 0.35, 0.01, 0.05, 0.07, 0.35, 0.49, 4.ix, 24.five, two.45 and 245.

ane, 5, 7, 35, 49, 245, 0.1, 0.5, 0.vii, 3.five, four.nine, 2.45, 0.01, 0.05, 0.07, 0.35, 0.49, and 2.45

The factor pairs of 2.45 are (1, ii.45), (5, 0.49), (vii, 0.35), (35, 0.07), (49, 0.05), (245, 0.01), (0.1, 2.45), (0.5, four.ix), and (0.7, 3.5).

Practice Problems

Cistron Pairs

Attend this Quiz & Examination your knowledge.

Correct answer is: ane
A prime number has only two factors i.e. ane and itself. Then, in that location is only i factor pair of a prime number.

(2, $\frac{ii}{11}$)

(ii, xi)

(1, $\frac{ii}{11}$)

(ii, $\frac{one}{11}$)

Correct answer is: (2, $\frac{two}{11}$)
2 ✕ $\frac{ii}{11}$ = $\frac{4}{11}$. So, (two, $\frac{two}{11}$) is a factor pair of $\frac{4}{11}$.

((ten-3),one)

(1,(ten-2))

((x+3),(x-2))

((x-iii),(x-two))

Correct answer is: ((x-3),(10-2))
x$^{ii}$ - 5x + 6 = 10$^{2}$ - 2x - 3x + half dozen = x(ten-2)-3(x-2) = (x-iii)(x-2)
Factors of x$^{2}$ - 5x + half-dozen are 1, (x-three),(x-two) and (x$^{2}$ - 5x + 6)
And so, ((ten-iii),(x-2)) is a factor pair of x$^{2}$ - 5x + 6.

Frequently Asked Questions

What is the difference between factors and factor pairs?

A number or algebraic expression that divides the another number or expression evenly is known as a factor. For example: Factors of 6 are 1, 2, 3 and half-dozen

On the other hand, a factor pair is the pair of the factors which when multiplied together gives the product. For case: Factor pairs of 6 are (1, 6) and (2, 3).

What are the minimum factor pair(s) of a composite whole number?

The minimum cistron pairs of a composite whole number are two.

Which numbers take merely ane gene pair?

Prime numbers have only one gene pair.