Factors and Multiples by using Multiplication Facts
Factors and multiples by using multiplication facts are explained here.
With the help of this operation we shall learn some other terms.
Consider the following factors and multiples by using multiplication facts:
(i) 3 × 5 = 15,
i.e., 3 multiplied by 5 gives the product 15.
Here, 3 is called the multiplicand, 5 is the multiplier and 15 is the product.
In 5 × 3 = 15, 5 is the multiplicand and 3 is the multiplier.
Thus, in any multiplication fact, multiplicand and multiplier may be interchanged. Both are known as factors. We can say 3 and 5 are the factors of 15. The product 15 may also be given the name of ‘multiple’. Thus, 15 is the multiple of the factors 3 and 5.
(ii) 1 × 15 = 15.
Here, 1 and 15 are the factors of multiple 15.
Thus, the multiple 15 has four factors, 1, 3, 5 and 15.
(iii) 1 × 3 × 5 = 15.
It also expresses that 1, 3 and 5 are the factors of 15.
(iv) 4 × 3 = 12,
i.e., 4 multiplied by 3 gives the product 12. We can say 4 and 3 are the factors of multiple 12.
Accordingly, 2 × 2 × 3 = 12, where 2, 2 and 3 are the factors of multiple 12.
also 1 × 2 × 2 × 3 = 12.
So 1, 2, 2 and 3 are the factors of 12.
1 × 2 × 6 = 12, or, 1 × 4 × 3 = 12 shows that 1, 2, 4, 6 are the factors of 12.
1 × 12 = 12
So, 1 and 12 are the factors of 12.
Hence, 1, 2, 3, 4, 6 and 12 are the factors of the multiple 12.
There are no other factors except 1, 2, 3, 4, 6 and 12 of multiple 12.
Any multiple has a definite number of factors.
12 has 6 factors, i.e., 1, 2, 3, 4, 6 and 12.
15 has 4 factors, i.e., 1, 3, 5 and 15.
More explanation:
David has 8 marbles. Let us see in how many ways David can arrange these marbles.
8 marbles in one row
|
|
8 × 1 = 8
|
4 marbles in two rows
|
|
4 × 2 = 8
|
2 marbles in four rows
|
|
2 × 4 = 8
|
The division facts for each of the multiplication facts are:
8 ÷ 1 = 8
8 ÷ 8 = 1
8 ÷ 2 = 4
8 ÷ 4 = 2
So, 8 is exactly divisible by 1, 2, 4 and 8.Therefore, 1, 2,
4 and 8 are factors of 8. A number is a factor of another number if it is an
exact divisor of the number. We can find factors of a number by multiplication
or by division method.
How to find the factors with the help of multiplication facts?
Using multiplication facts,
(i) Factor Factor Multiple
7 × 9 = 63
(ii) Factor Factor Multiple
8 × 4 = 32
(iii) Factor Factor Multiple
6 × 5 = 30
We learnt that the product of the two numbers is the multiple of each of the numbers.
In other words: each of the numbers is the factor of the multiple.
(i) 7 and 9 are factors of 63
(ii) 8 and 4 are factors of 32
(iii) 6 and 5 are factors of 30
Note:
Any number which can be divided into a bigger number without leaving a remainder is a factor of the bigger number.
● Let us find the factors of 24 by multiplication method.
1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24
● Find all the factors of 64 by multiplication method.
64 = 1 × 64
64 = 2 × 32
64 = 4 × 16
64 = 8 × 8
Hence, all the factors of 64 are 1, 2, 4, 8, 16, 32, 64.
You might like these
-
We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us consider two numbers 16 and 24.
-
In 4th grade factors and multiples worksheet we will find the factors of a number by using multiplication method, find the even and odd numbers, find the prime numbers and composite numbers, find the prime factors, find the common factors, find the HCF(highest common factors
-
Examples on multiples on different types of questions on multiples are discussed here step-by-step. Every number is a multiple of itself. Every number is a multiple of 1. Every multiple of a number is either greater than or equal to the number. Product of two or more numbers
-
In worksheet on word problems on H.C.F. and L.C.M. we will find the greatest common factor of two or more numbers and the least common multiple of two or more numbers and their word problems. I. Find the highest common factor and least common multiple of the following pairs
-
Let us consider some of the word problems on l.c.m. (least common multiple). 1. Find the lowest number which is exactly divisible by 18 and 24. We find the L.C.M. of 18 and 24 to get the required number.
-
Let us consider some of the word problems on H.C.F. (highest common factor). 1. Two wires are 12 m and 16 m long. The wires are to be cut into pieces of equal length. Find the maximum length of each piece. 2.Find the greatest number which is less by 2 to divide 24, 28 and 64
-
The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is the smallest of all common multiples.
-
Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, …………etc. Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, …………… etc.
-
In worksheet on multiples of that numbers, all grade students can practice the questions on multiples. This exercise sheet on multiples can be practiced by the students to get more ideas on the numbers that are being multiplied. 1. Write any four multiples of: 7
-
Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor. When a number is expressed as the product of its prime factors, it is called prime factorization. For example, 6 = 2 × 3. So 2 and 3 are prime factors
-
Prime factor is the factor of the given number which is a prime number also. How to find the prime factors of a number? Let us take an example to find prime factors of 210. We need to divide 210 by the first prime number 2 we get 105. Now we need to divide 105 by the prime
-
The properties of multiples are discussed step by step according to its property. Every number is a multiple of 1. Every number is the multiple of itself. Zero (0) is a multiple of every number. Every multiple except zero is either equal to or greater than any of its factors
-
What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.
-
Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers. (i) 6 and 8 (ii) 9 and 15 (iii) 16 and 18 (iv) 16 and 28
-
In this method we first divide the greater number by the smaller number. The remainder becomes the new divisor and the previous divisor as the new dividend. We continue the process until we get 0 remainder. Finding highest common factor (H.C.F) by prime factorization for
Related Concept
● Factors
and Multiples by using Multiplication Facts
● Factors
and Multiples by using Division Facts
● Multiples
● Properties of
Multiples
● Examples on
Multiples
● Factors
● Factor Tree Method
● Properties of
Factors
● Examples on
Factors
● Even and Odd
Numbers
● Even
and Odd Numbers Between 1 and 100
● Examples
on Even and Odd Numbers
4th Grade Math Activities
From Factors and Multiples by using Multiplication Facts to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
Share this page:
What’s this?
|
|
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.