Determine if 96810 is divisible by 48.
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Answer:
no it is not divisible by 48
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Answer:
A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. It also tells us the remainder we get when a number is divided by a given number
1.Divisibility by 2n : If the last n digits of the number is divisible by 2n, then the number is divisible by 2n.
a. 21 – For 2, we check the last digit. Last digit should be divisible by 2. The last digit is even (0, 2, 4, 6, or 8)
b. 4 - 4 can be written as 22. So divisibility rule of 4 says check the last 2 digits. If the last 2 digits of a number is divisible by 4 then the whole number is divisible by 4.
c. 8 - 8 can be written as 23. So divisibility rule of 8 says check the last 3 digits. If the last 3 digits of a number is divisible by 8 then the whole number is divisible by 8.
Ex. 953360 is divisible by 8, since the number formed by last three digits is 360, which is divisible by 8. But, 529418 is not divisible by 8, since the number formed by last three digits is 418, which is not divisible by 8.
d. 16 - 16 can be written as 24. So divisibility rule of 16 says check the last 4 digits. If the last 4 digits of a number is divisible by 16 then the whole number is divisible by 16.
So, this divisibility rule is applicable for all the powers of 2.
So we now have the divisibility rule for 2,4,8,16,32,64,128,256,512,.......
2. Divisibility rule of 3 and 9
A number is divisible by 3, if the sum of its digits is divisible by 3.
A number is divisible by 9, if the sum of its digits is divisible by 9.
Ex.592482 is divisible by 3, since sum of its digits =(5+9+2+4+8+2)=30, which is divisible by 3.
But, 864329 is not divisible by 3, since sum of its digits =(8+6+4+3+2+9)=32, which is not divisible by 3.
Ex. 60732 is divisible by 9, since sum of digits =(6+0+7+3+2)=18, which is divisible by 9.
But, 68956 is not divisible by 9, since sum of digits =(6+8+9+5+6)=34, which is not divisible by 9.
3. Divisibility rule of 5n: If the last n digits of the number is divisible by 5n, then the number is divisible by 5n.
5 - A number is divisible by 5, if its unit's digit is either 0 or 5. Thus, 20820 and 50345 are divisible by 5, while 30934 and 40946 are not.
25 – Can be written as 52. So for 25, we check the last 2 digits. If the last 2 digits of a number is divisible by 25 then the complete number is divisible by 25.
125 - Can be written as 53. So for 125, we check the last 3 digits. If the last 3 digits of a number is divisible by 125 then the complete number is divisible by 125.
625 - Can be written as 54. So for 625, we check the last 4 digits. If the last 4 digits of a number is divisible by 625 then the complete number is divisible by 625.
So, this divisibility rule is applicable for all the powers of 5.
So we now have the divisibility rule for 5,25,125,625,3125,.......
4. Divisibility rule of 7: To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number. Repeat the process till we get a 3 digit number. If the number is divisible by 7 (including zero), then the original number is divisible by 7.
5. Divisibility By 10:
A number is divisible by 10, if it ends with 0.Ex. 96410, 10480 are divisible by 10, while 96375 is not.
6. Divisibility By 11:
A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.
Ex. The number 4832718 is divisible by 11, since :(sum of digits at odd places) - (sum of digits at even places) =
=(8+7+3+4)−(1+2+8)=11, which is divisible by 11.
7. Divisibility Rule of 13: To find out if a number is divisible by 13, take the last digit, double it, and add it to the rest of the number. Repeat the process till we get a 3 digit number. If the number is divisible by 13 (including zero), then the original number is divisible by 13
8. Divisibility by 17 : Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978-->397-5*8=357-->35-5*7=0. So 3978 is divisible by 17.
9. Divisibility by 19: Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.
EG: 101156-->10115+2*6=10127-->1012+2*7=1026-->102+2*6=114 and 114=6*19, so 101156 is divisible by 19.
10. Divisibility by composite numbers:
Find two coprime factors of the composite number and the apply the divisibility rule of these factors.
Ex- 6 = 2 x 3. So a number is divisible by 6 if it is divisible by both 2 and 3
12= 3x4. So a number is divisible by 12 if it is divisible by both 3 and 4
18=2x9. So a number is divisible by 18 if it is divisible by both 2 and 9
48= 16x3. So a number is divisible by 48 if it is divisible by both 16 and 3
72= 8x9. So a number is divisible by 72 if it is divisible by both 8 and 9