How to find factor by multiplication ?
Answers
Answer:
Prime Numbers
A number that can only be divided by 1 and itself is called a prime number. Examples of prime numbers are 2, 3, 5, 7, 11 and 13. The number 1 is not considered a prime number because 1 goes into everything.
Divisibility Rules
Some divisibility rules can help you find the factors of a number. If a number is even, it's divisible by 2, i.e. 2 is a factor. If a number's digits total a number that's divisible by 3, the number itself is divisible by 3, i.e. 3 is a factor. If a number ends with a 0 or a 5, it's divisible by 5, i.e. 5 is a factor.
If a number is divisible twice by 2, it's divisible by 4, i.e. 4 is a factor. If a number is divisible by 2 and by 3, it's divisible by 6, i.e. 6 is a factor. If a number is divisible twice by 3 (or if the sum of the digits is divisible by 9), then it's divisible by 9, i.e. 9 is a factor.
Finding Factors Quickly
Establish the number you want to find the factors of, for example 24. Find two more numbers that multiply to make 24. In this case, 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24. This means the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Factor negative numbers in the same way as positive numbers, but make sure the factors multiply together to produce a negative number. For example, the factors of -30 are -1, 1, -2, 2, -3, 3, -5, 5, -6, 6, -10, 10, -15 and 15.
If you have a large number, it's more difficult to do the mental math to find its factors. To make it easier, create a table with two columns and write the number above it. Using the number 3784 as an example, start by dividing it by the smallest prime factor (bigger than 1) that goes into it evenly with no remainder. In this case, 2 x 1892 = 3784. Write the prime factor (2) in the left column and the other number (1892) in the right column.
Continue with this process, i.e. 2 x 946 = 1892, adding both numbers to the table. When you reach an odd number (e.g., 2 x 473 = 946), divide by small prime numbers besides 2 until you find one that divides evenly with no remainder. In this case, 11 x 43 = 473. Continue the process until you reach 1.
Answer:
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
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.
Step-by-step explanation: