Patterns in the multiples of 2, 5, 10 and 3

Recognizing patterns in the multiple of 2, 5, 10, and 3 is helpful.

multiples of 2

2 x 1 = 2
2 x 2 = 4
2 x 3 = 6
2 x 4 = 8
2 x 5 = 10
2 x 6 = 12
2 x 7 = 14
2 x 8 = 16
2 x 9 = 18
2 x 10 = 20

The last digit of any multiple of 2 is 0, 2, 4, 6, or 8. so if you want to find out 456 is a multiple of 2, check the last digit is 0, 2, 4, 6, or 8. which is, in this case, is 6 and 456 is a multiple of 2. simple right?

2 * 228 = 456

multiples of 3

3 x 1 = 3
3 x 2 = 6
3 x 3 = 9
3 x 4 = 12
3 x 5 = 15
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
3 x 9 = 27
3 x 10 = 30

unlike the patterns of 2, 5, and 10 patterns of 3 is not based on the last digit. the pattern of 3 is based on the sum of the digits. if the sum is a multiple of 3 then the number is a multiple of 3.

e.g. 372 3+7+2 = 12 12 is a multiple of 3. so 372(3 x 124) is a multiple of 3.

multiples of 5

5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30
5 x 7 = 35
5 x 8 = 40
5 x 9 = 45
5 x 10 = 50

multiples of 5 end with either 5 or 0.

multiples of 10

10 x 1 = 10
10 x 2 = 20
10 x 3 = 30
10 x 4 = 40
10 x 5 = 50
10 x 6 = 60
10 x 7 = 70
10 x 8 = 80
10 x 9 = 90
10 x 10 = 100

The multiples of 10 end with 0.

notice that the multiples of 10 are the numbers that are multiples of both 2 and 5. That's because 10 = 2 x 5. the same principle applies to multiples of 6. if a number is a multiple of both 3 and 2 then that number is a multiple of 6.