# What are the tests of divisibility for 7 and 12? Apply the test of divisibility by 7 for 48895 and 12 for 43490.

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**1. Test of divisibility by 7: ** Double the last digit of the number and subtract it from the remaining truncated number, if the remainder is divisible by 7 then the number is divisible by 7. Eg: 742. Double the last digit =4, subtract 4 from the truncated number 74 = 70 which is divisible by 7, therefore 742 is divisible by 7.

48895

Doubling the last digit 5 = 10,

subtract 10 from the truncated number 4889 = 4879

divide 4879 by 7 = 697

therefore 48895 is divisible by 7.

** 2.Test of divisibility by 12:** The number must be divisible by 4 and 3. The test of divisibility for 4 is that the last two digits must be divisible by 4. The test of divisibility for 3 is that the sum of the digits must be divisible by 3. Eg: 1272. The last two digits 72 are divisible by 4 which = 18 and the sum of the digits 12 is divisible by 3 which = 4, therefore 1272 is divisible by 12.

43490

the last two digits 90 are not divisible by 4

the sum of the digits 20 is also not divisible by 3

therefore 43490 is not divisible by 12.

48895:To see whether it is divisible by 7:

Make Groups of 3 digits from unit place towards left: 895 is the first group and the second group is 48 or 045. First group - 2nd group= 895-48=847 which is divisible by 7. So, 48,895 is also divisible by 7.

43490: To test the divisibility by 12.

The sum of the digits is 4+3+4+9+0 =20. The sum of digits in 20 =2+0=2 . So ultimately arrived at digit is 2 and it is not divisible by 3. It is a necessary condition that a number which is divisible by 12 must be divisible by 3 also.So, the number 43490 is also not divisible by 12. (Also the 2 digit ending number 90 in 434**90 **is not divisible by 4. So, the number could not be divisible by 12 by similar rasoning as the preceding one). But one condition is sufficient to establish that the given number has no divisibility by 12.