Multiples

A multiple is a number that may be divided by another number several times without leaving a residue.

A factor is a number that divides a given number without leaving a remainder.

Twenty is a multiple of five and a multiple of four, according to a number sentence.

It also informs us that 5 and 4 are 20-factors.

Multiples and factors have a connection. The number that divides a number fully without leaving any residual is called a factor. We can write p q = z for any number. z is a multiple of p and q in this case. Because z is divisible by both p and q, p and q are factors of z, according to the definition of factors and multiples. 6 x 2 = 12, for example, means that 6 and 2 are factors of 12, and 12 is a multiple of 6 and 2.

How do you find multiples and factors?

To identify factors and multiples of any given integer, such as ‘p,’ we must first find a list of numbers that divide ‘p’ without leaving any leftover. Take number 28 as an example. How can we find 28 factors?

Steps to Finding a Number’s Factors

Step 1: Add the two numbers together to get 28.

Step 2: Consider the numbers 4 and 7.

Step 3: In this case, 28 is evenly divisible by 4 and 7, with no remainder.

Step 4: 28 = 7 4 can now be factored in.

Step 5: There are also finite numbers that can be used to divide an integer without leaving a residue. Make a list. The digits 1, 2, 4, 7, 14, and 28 are used in this situation.

Step 6: Numbers 1, 2, 4, 7, 14, and 28 are all factors of 28.

The factors of the relevant numbers are always 1 and the number itself.

Finding Multiples of a Number

The numbers we get when multiplying a number by a whole number are called multiples of that number. Let’s use number 28 as an example. What is the best way to find 28 multiples? The numbers that follow from multiplying 28 by another whole number are referred to as multiples of 28. Consider the following skip counting procedure. The skip counting method is one of the most basic ways to determine multiples of a given number.

Common Factors and Multiples

Find common factors and multiples of any number in this area. A factor is defined as an integer that divides a given number exactly. As a result, a factor is simply the number’s divisor. Both multiplication and division can be used to find the factors. Follow the steps below to see if two or more numbers have similar factors:

Put the numbers in the correct order.

Make a list of all the numbers’ possible factors.

Find the numbers that have the same factors.

Surround the common factors with a circle.

Properties of Factors and Multiples

Many properties of factors and multiples will aid in your understanding of this idea. Below is a list of those properties:

Every number is multiplied by 1.

Every number has a multiple of 0.

Only full numbers are factored or multiplied.

The smallest factor for any number is 1 and the largest factor is the number itself.

Every number is a multiple of another number.

For each number, there exist infinite multiples and a finite number of factors.

A prime number is one that has just two elements, namely 1 and the number itself.

Multiples with the same value for two or more numbers are called common multiples.

What are the most common two-digit and three-digit multiples?

6, 12, 18,… are some of the most common multiples of 2 and 3.

Common multiples can go on forever.

The smallest multiple shared by two or more numbers is known as the least common multiple (LCM).

What is the smallest multiple of two and three?

Both 2 and 3 have the same smallest multiple, which is 6.

Conclusion 

Any number’s multiples are limitless. As a result, an unlimited number of common multiples can exist for any pair of numbers.

The smallest common multiple of any two or more numbers is known as the Least Common Multiple (LCM). The LCM of 3 and 4 is, for instance, 12.

A factor is a number or quantity that creates a specified number or expression when multiplied by another. a number that may be divided by another without leaving a residue.