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Using divisibility tests, determine which of the following numbers are divisible by 6:
(a) 297144   (b) 1258   (c) 4335   (d) 61233
(e) 901352   (f) 438750   (g) 1790184   (h) 12583
(i) 639210   (j) 17852

Solution:

We will be using the concepts of divisibility by 6 to solve this.

We know that a number is divisible by 6 if it is divisible by both 2 and 3.

(a) Given number = 297144
The number 297144 has an even digit at its one's place.
Therefore, it is divisible by 2.
The sum of all the digits of 297144 = 2 + 9 + 7 + 1 + 4 + 4 = 27, which is divisible by 3.
Therefore, the number 297144 is divisible by 6.

(b) Given number = 1258
The number 1258 has an even digit i.e., 8 at its one's place.
Therefore, it is divisible by 2.
The sum of all digits of 1258 = 1 + 2 + 5 + 8 = 16, which is not divisible by 3.
Therefore, the number 1258 is not divisible by 6.

(c) Given number = 4335
The digit at one's place of the number 4335 is not even.
Therefore, it is not divisible by 2.
Therefore, the number 4335 is not divisible by 6.

(d) Given number = 61233
The digit at one's place of the number 612333 is not even.
Therefore, it is not divisible by 2.
The number 61233 is not divisible by 6.

(e) Given number = 901352
The digit at one's place of the given number is even, i.e, 2
Therefore, it is divisible by 2.
The sum of all the digits of the number 901352 = 9 + 0 + 1 + 3 + 5 + 2 = 20, which is not divisible by 3.
Therefore, the number 901352 is not divisible by 6.

(f) Given number = 438750
The digit at one's place of the number 438750 is 0.
Therefore, it is divisible by 2.
The sum of all the digits of the number 438750 = 4 + 3 + 8 + 7 + 5 + 0 = 27, which is divisible by 3.
Therefore, the number 438750 is divisible by 6.

(g) Given number = 1790184
The digit at one's place of the number 1790184 is even i.e, 4.
Therefore, it is divisible by 2.
The sum of all the digits of the number 1790184 = 1 + 7 + 9 + 0 + 1 + 8 + 4 = 30 which is divisible by 3.
Therefore, the number 1790184 is divisible by 6.

(h) Given number = 12583
The digit to one's place of the number 12583 is odd.
Therefore, it is not divisible by 2.
Therefore, the number 12583 is not divisible by 6.

(i) Given number = 639210
The digit at one's place of the number 639210 is 0.
Therefore, it is divisible by 2.
The sum of all the digits of the number 639210 = 6 + 3 + 9 + 2 + 1 + 0 = 21, which is divisible by 3.
Therefore, the number 639210 is divisible by 6.

(j) Given number = 17852
The digit at one's place of the number 17852 is even.
Therefore, it is divisible by 2.
The sum of all the digits of the number 17852 = 1 + 7 + 8 + 5 + 2 = 23, which is not divisible by 3.
Therefore, the number 17852 is not divisible by 6.

You can also use the Online Divisibility Calculator to check this.

NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 Question 3

Using divisibility tests, determine which of the following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352 (f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

Summary:

The numbers divisible by 6 are (a) 297144 (f) 438750 (g) 1790184 (i) 639210

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