Ppt On Factors And Multiples Free Download _BEST_
Brigitte Bjork
Factors and multiples are two interrelated concepts in mathematics. If $A \times B = C$, then A and B are factors of C, whereas C is a multiple of both A and B.
A multiple is a result of multiplying a number by an integer. Note that, when we study multiples of any number, we generally talk about positive multiples only (excluding 0 and negative multiples). Thus, we can say that a multiple is the number obtained by multiplying a given number by a positive integer.
Factors and multiples can be used in many real-life situations, such as finding the number of seats in a theater or the number of tiles needed to cover a floor. They are also important in mathematical concepts like fractions, ratios, and proportions.
Mathematics is a game of numbers, where we study number, its types and the concepts relating to it. Arithmetic is that branch of mathematics which focuses on properties and manipulation of numbers. Factors and multiples are two key concepts studied together in arithmetic, at the elementary level. A factor is a number that leaves no remainder behind after it divides the specific number.
Basis for ComparisonFactorsMultiplesMeaningFactor refers to an exact divisor of the given number. Multiple alludes to the result we get, when we multiply a given number by another number.What is it?It is a number that can be multiplied to get another number.It is a product obtained after multiplying the number by an integer.Number of factors/multiplesFiniteInfiniteOutcomeLess than or equal to the given number.Greater than or equal to the given number.Operation usedDivisionMultiplication
To find out multiples of a given number, you need to multiply that particular number by integers beginning with number 1. The resultant number, after the multiplication of the given numbers, is the multiple of the given number.
Suppose there are two number 2 and 6, where 2 is the factor of 6, then 6 will essentially be a multiple of 2. Hence, by this explanation, you might have understood that a number is a multiple of all its factors, like in our example 6 is a multiple of all its factors, i.e. 1, 2, 3 and 6.
To sum up, we can say that factors are the numbers that can be multiplied to get another number. On the other hand, multiples are the product, that one can get by multiplying a number with another. When a number possesses only two factors, i.e. 1 and itself, then that number will be known as a prime number.
What is a multiple? A multiple of a number is the result when that number is multiplied by an integer. Compared to the factor examples above, where 4 is a factor of 8 and 12, 8 and 12 are multiples of 4.
Common multiples are multiples shared between two or more given numbers. For example, 24 is a common multiple of 2, 3 and 6 as it is a multiple of all three numbers (note that 2, 3 and 6 are also all factors of 24).
The least common multiple (LCM), also referred to as the lowest common multiple, is the smallest multiple shared between two or more given numbers. For example, the least common multiple of 10 and 15 is 30 as it is the smallest multiple that both given numbers share (10 x 3 = 30 and 15 x 2 = 30). Least common multiples can be used to express fractions in the same denomination, which is useful when they are being added or subtracted.
Common factors are factors shared between two or more given numbers. For example, 5 is a common factor of 5, 10 and 25 as it is a factor of all three numbers (note that 5, 10 and 25 are also all multiples of 5).
The greatest common factor (GCF), also referred to as the highest common factor, is the largest factor shared between two given numbers. For example, the greatest common factor of 15 and 20 is 5 as it is the largest number that both given numbers can be divided by without remainders. Greatest common factors can be used to simplify fractions.
Every number has a set amount of factors. First, every number has a factor of 1. Numbers with only two factors (1 and themselves) are called prime numbers. Numbers with more than two factors are called composite numbers. There are a few ways to find all the factors of a given number.
To find all the factors of a given number, start with 1 and systematically work through each number to see if it has a factor pair that will multiply to make the given number, until the factors end up repeating themselves. For example, to find all the factors of 24:
In Year 5, children will continue to carry out tasks involving factors and multiples and this will extend to learning about prime numbers and square numbers.
By Year 6 children need to be really confident not only on knowing what factors and multiples are, but also on quickly working out the factors and multiples of various numbers. This means they can take quickly to these sorts of puzzles. They might able be asked to find the lowest common multiple or highest common factor of two numbers or a group of numbers.
Some children found chains of 24 by finding multiples then factors and repeating this.
Some children found chains of 36 through just randomly finding factors and multiplying and working through the process of elimination.
Factors and multiples are related to each other. A factor of a number is the number that divides it completely without leaving any remainder. For any given number we can represent it as p q = z. Here we say z is a multiple of p and q. According to the definition of factors and multiples, p and q are factors of z, because z is divisible by p as well as q. For example, 6 2 = 12, so 6 and 2 are the factors of 12, and 12 is a multiple of 6 and 2.
To find factors and multiples of any given number, let say 'p', we have to find the list of numbers that divide the number 'p' without leaving any remainder. Here let us take an example of number 28. How can we find factors of 28?
Multiples of a number are the numbers that we get after multiplying the number by a whole number. Here, let us take the same example of number 28. How can we find multiples of 28? The multiples of 28 are all the numbers that result from the multiplication of 28 by another whole number. Let us look at the skip counting method shown in the image below. The skip counting method is one of the simplest methods to find the multiples of any given number.
In this section, you will learn how to find common factors and multiples of any number. We know that a factor is a number that exactly divides the given number. Hence, a factor is nothing but a divisor of the given number. To find the factors, we can use the multiplication as well as the division method. To check if two or more numbers have common factors between them we can follow the below steps:
Let us use the Venn diagram method. First, mark the multiples of any 2 numbers, let's say 3 and 4 in two separate circles. Look for the common numbers coming in both circles. The circle of multiples of 3 intersects with the circle of multiples of 4. The intersection part has the common multiples that belong to 3 as well as 4. Please note that there are infinite numbers of common multiples for every pair of numbers. The first three common multiples of 3 and 4 are 12, 24, and 36.
Solution:
As per the definition of common factors and multiples, the common multiples of 3 and 4 are equal to the multiples of LCM of 3 and 4. The LCM of 3 and 4 is 12. All the multiples of 12 which are less than 100 are 12, 24, 36, 48, 60, 72, 84, and 96.
Therefore, the common multiples of 3 and 4 are 12, 24, 36, 48, 60, 72, 84, and 96.
The factors of 60 are all the whole numbers that can divide 60 without leaving any remainder. So, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The mutiples of 60 can be found by multiplying 60 with whole numbers starting from 1.
60 1 = 60
60 2 = 120
60 3 = 180
60 4 = 240
60 5 = 300
So, the list of multiples of 60 includes 60, 120, 180, 240, 300, and so on.
Therefore, the factors and multiples of 60 are:
Factors = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
Multiples = 60, 120, 180, 240, 300, ...
Solution: To find the common factors and multiples of 4, 8, and 12 we will use the listing method.
Let us write separately factors of 4,8 and 12. There are 3 factors of 4 which are 1, 2, and 4. There are 4 factors of 8 listed as 1, 2, 4, and 8. There are 6 factors of 12 which are 1, 2, 3, 4, 6, and 12.
The common factors of 4, 8, and 12 are 1, 2, and 4.
Let us make a list of multiples of 4, 8, and 12.
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72 ...
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 ...
Multiples of 12 = 12, 24, 36, 48, 60, 72, ...
So, the common multiples of 4, 8, and 12 are 24, 48, 72, ...
Factors and multiples are two related concepts in math. A factor is a number that divides the given number exactly with 0 as the remainder. And a multiple is a number that is obtained by multiplying the given number with any whole number. For example, if it is given that 5 6 = 30. Here, 30 is the multiple of 5 and 6, and 5, and 6 are the factors of 30.
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