Question

A
(0) 14500 921004 LJ 31195012
11 sing divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335
(d) 61233 (e) 901352
438750 g 1790184 (h) 12583 (1) 639210 (1) 17852​

Answer 1

Step-by-step explanation:

Given number is divisible by 6 if it is divisible by both 2 and 3.

We can clearly see that 4335, 61233 and 12583 are the numbers which are not divisible by 2 because the last digit is not 0, 2, 4, 6 or 8. Therefore, we can ignore all these numbers.

Rest of the numbers are divisible by 2 which are 297144, 1258, 901352, 438750, 1790184, 639210 and 17852.

Now, we want to select numbers from the remaining list which are divisible by 3.

Given number is divisible by 3 if the sum of digits is multiple of 3.

For number 297144, sum of digits = 2 + 9 + 7 + 1 + 4 + 4= 27 which is multiple of 3. We showed above that 297144 is the number which is also divisible by 2. Hence, it is also divisible by 6.

For number 1258, sum of digits = 1 + 2 + 5 + 8 = 16 which is not a multiple of 3. Therefore, 1258 is not divisible by 3. Hence, it is not divisible by 6.

For number 901352, sum of digits = 9 + 0 + 1 + 3 + 5 + 2 = 20 which is not a multiple of 3. Therefore, 901352 is not divisible by 3. Hence, it is not divisible by 6.

For number 438750, sum of digits = 4 + 3 + 8 + 7 + 5 + 0 = 27 which is multiple of 3. Therefore, 438750 is divisible by 3. We showed above that it is also divisible by 2. Hence, it is also divisible by 6.

For number 1790184, sum of digits = 1 + 7 + 9 + 0 + 1 + 8 + 4 = 30 which is multiple of 3. Therefore, 1790184 is divisible by 3. We showed above that it is also divisible by 2. Hence, it is also divisible by 6.

For number 639210, sum of digits = 6 + 3 + 9 + 2 + 1 + 0 = 21 which is multiple of 3. Therefore, 639210 is divisible by 3. We showed above that it is also divisible by 2. Hence, it is also divisible by 6.

For number 17852, sum of digits = 1 + 7 + 8 + 5 + 2 = 23 which is not a multiple of 3. Therefore, 17852 is not divisible by 3. Hence, it is not divisible by 6.

From the discussion above, we can say that (a), (f), (g) and (i) are the numbers which are divisible by 6.

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