For example, 30 = 3 × 10, so 3 and 10 are factors of 30 and 30 is a multiple of 3 and 10
Take note that 1 is a factor of every number.
Understanding factors and multiples is essential for solving many math problems.
For example, the prime factorization of 180 is 2 × 2 × 3 × 3 × 5
You can use repeated division by prime numbers to obtain the prime factors of a given number.
For example, to get the GCF of 24, 60 and 66:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
The factors of 66 are 1, 2, 3, 6, 11, 22,33 and 66
Look for the greatest factor that is common to all three numbers - thus 6 is the GCF of 24, 60 and 66.
As the name implies, we need to list the multiples and to find the least one that is common to all the numbers.For example, to get the LCM of 3, 6 and 9:
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21 ...The multiples of 6 are 6, 12, 18, 24, ...
The multiples of 9 are 9, 18, 27, ...
Look for the least multiple that is common to all three numbers - thus 18 is the LCM of 3, 6 and 9.
Shortcut To Finding LCM
Here is a useful shortcut (also called the ladder method) to finding the LCM of a set of numbers. For example, to find the LCM of 3, 6 and 9, we divide them by any factor of the numbers in the following manner:
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