Tests for divisibility of numbers - 6th class

Tests for divisibility of numbers

Divisibility by 2:  A number is divisible by 2, if the digit in its unit's place is divisible by 2. Hence, this number must be even and so the digit in the unit's place of this number must be 0, 2, 4, 6 or 8. Other numbers which end with the digits 1, 3, 5, 7 or 9 will not be divisible by 2. Thus, numbers like 20592, 31296, 802598, etc. are all divisible by 2. 

Divisibility by 3: A number is divisible by 3, if the sum of the digits of this number is divisible by 3. For example, 409362, 523758, etc. are all divisible by 3. For, the sum of the digits of the 1st number is 4 + 0 + 9 + 3 + 6 + 2 = 24 which is divisible by 3. Similarly, the sum of the digits of the 2nd number is 5 + 2  + 3 + 7 + 5 + 8 = 30, which is divisible by 3.

Divisibility by 9: A number is divisible by 9, if the sum of the digits of this number is divisible by 9. For example, 8208 is divisible by 9, for, 8 + 2 + 0 + 8 = 18 is divisible by 9. 

Divisibility by 5: A number is divisible by 5, if the digit in its unit's place is 0 or 5. For example, 30590, 8935, etc. are all divisible by 5. A number whose unit's digit is other than 0 or 5 is not divisible by 5. Thus, 31574, 8932, etc. are not divisible by 5. 

Divisibility by 10: A number whose unit's digit is 0 is divisible by 10. A number whose unit's digit is not 0 is not divisible by 10. Thus, 3890, 52300, etc. are all divisible by 10, but 31925, 73212, etc. re not divisible by 10. 

Divisibility by 11: A number is divisible by 11, if the difference of the sum of its digits in odd places and the sum of its even places starting from the unit's place is divisible by 11. For example, we take the following numbers: (1) 107877 and (2) 35849. In 107877 the digits in the odd places are 7, 8, 0 and those in the even places are 7, 7 and 1. Therefore, the sum of the digits in odd places = 7 + 8 + 0 = 15 and the sum of the digits in even places = 7 + 7 + 1 = 15. Difference of the two sums = 15 -  15 = 0 which is divisible by 11. Hence, the given number 107877 is divisible by 11.In 35849,  the sum of the digits in the odd places = 9 + 8 + 3 = 20 and the sum of the digits in the even places = 4 + 5 = 9. The difference of the two sums = 20 - 9 = 11 which is divisible by 11. 

Divisibility by 4:  A number is divisible by 4, if the number formed by its digits in ten's place and unit's place is divisible by 4. Thus, the numbers like 532, 2316, 89372, etc. are all divisible by 4, since 32, 16, 72 are divisible by 4. 

Divisibility by 8:  A number is divisible by 4, if the number formed by its digits in hundred's place, ten's place and unit's place is divisible by 8. Thus, the numbers 5720, 26824, 357128, etc. are all divisible by 8, since 720, 824, 128 are all divisible by 8.

Divisibility by 6:  A number is divisible by 4, if it is divisible by both 2 and 3. Clearly, the number should be even and the sum of its digits should be divisible by 3. For example, the numbers 2256, 41568, 980352, etc, are ll divisible by 6, since all these numbers are even and the sum of the digits of each number is divisible by 3.