Hello there. In this math post I go over the divisibility rules for determining if a whole number is divisible by 4, 9 or 10.
Knowing If You Can Take A Quarter Of A Number
The divisibility rule for 4 is not too difficult. There are two ways to determine if you can divide a number by 4.
Method One
Take half of the number first. Then take half of that half. If this half of the half is a whole number then the original (larger) number is divisible by 4.
Consider the number 120 as an example. Half of 120 is 60. Taking half of 60 is 30. Since 30 is a whole number, this means that 120 is divisible by 4.
Method Two
A more common and easier method considers the digits of the number. If the last two digits in the number is a multiple of 4 (4, 8, 12, 16, etc.) then that number is divisible by 4. In addition if the last two digits are zeroes, the number is also divisible by four.
The number 120 has its last two digits as 20. Because 20 is a multiple of 4 we can conclude that 120 is a multiple of 4.
The number 2000 is divisible by 4 due to the ending zeroes as the last two digits.
Divisibility Rule For 8
The divisibility rule for 8 is similar to method two for the divisibility rule for 4. Check if the last three digits of a number is a multiple of 8.
Example One
The number 1064 has the last three digits as 064. This number of 64 is a multiple of 8 (8 x 8) which means that the number 1064 is divisible by 8.
Example Two
Consider a larger number such as 10808. The last three digits form the number 808 which is a multiple of 8. It can be concluded that the number 10808 is divisible by 8.
Divisibility Rule For 9
To see if a number can be divided by 9 simply add all the digits together in that number. If the total/sum of the digits is a multiple of 9 then the number is divisible by 9.
As an example use the number 729. Adding the digits in 729 gives 7 + 2 + 9 = 18. The number 18 is a multiple of 9 which means that the number 729 is divisible by 9.
Divisibility Rule For 10
Knowing if a number can be divided by 10 is really easy. Given a number that is 10 or higher, a number that ends with a 0 is divisible by 10.
Numbers such as 20, 100, 2030, 300, 330, and something big as in 1 734 030 are divisible by 10.
