Math Lesson 1.5.1 - What are Multiples of a Number? What are Factors?

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Welcome to our Math lesson on What are Multiples of a Number? What are Factors?, this is the first lesson of our suite of math lessons covering the topic of Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

What are Multiples of a Number? What are Factors?

Before giving the definition of multiples of a number, we will look at the times table and explain how to use the times table. The times table is a table that includes all results obtained when multiplying numbers, normally, up to 10 with each other. Did you know - We use 10 for the times table because we frequently work with decimalisation (weights, units and measurements in groups of 10), in the UK, older generations will remember learning the times table up to 12, this was to make mental arithmetic with the imperial measurement system easier.

Let's explain the times table in simple words: multiples of a number are written next to those numbers that are in the same row (or column) in the times table. For example, in the row corresponding to the number 5 (where this number is at the leftmost position) we have written the numbers 5, 10, 15, 20, 25, etc. All of these numbers are multiples of 5. You can use a times table as a quick calculation reference by finding the first number you wish to multiply in the column on the left, then trace you finger along the times table to the column which mathes the second number in your multiplication equation. This will then provide you the answer to that multiplication. For example what is 4 x 7? In the first grey column, place you finger on the row with number four, now move your finger 7 places to the right. Your finger will now be resting on the square with 28 written in it, so, 4 x 7 = 28. The times table is a very simple calculation tool and has, in the past, been written out with numbers in their thousands. These times tables were used for specific calculations in science, meteorology and cosmology but they are now almost obsolete as the same calculations are completed with a calculator. It is however important to understand the basic 10 by 10 times table to help you improve your mental arithmetic.

In more formal terms, multiples of a number N are those numbers, which the number N divides without remainder.

Factors on the other hand, are the inverse of multiples. Thus, since 24 is a multiple of 4, then 4 is a factor of 24. By definition, a factor is a divisor of a number if the division is done without a remainder.

We have mentioned the term "factor" in previous topics, when we gave the names of participants in a multiplication. We said that two or more factors are multiplied to give a product. From here, we can imply that factors are divisors of a number.

Example 1

Find all multiples of 4 between 27 and 49.

Solution 1

Multiples of 4 are those numbers that are divisible by 4. They are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, etc. From all these numbers, only 28, 32, 34, 40, 44 and 48 are between 27 and 49.

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