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# Using divisibility tests, determine which of 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

To do :

We have to find whether the given numbers are divisible by 6.

Solution :

Divisibility rule of 6:

Numbers that are divisible by both 2 and 3 are divisible by 6.

That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.

(a) 297144

The number is divisible by 2 as the last digit is 4.

The sum of digits is $2+9+7+1+4+4 = 27$, which is also divisible by 3.

Hence, 297144 is divisible by 6.

(b) 1258

The number is divisible by 2 as the last digit is 8.

The sum of digits is $1+2+5+8 = 16$, which is not divisible by 3.

Hence, 1258 is not divisible by 6.

(c) 4335

The number is not divisible by 2 as the last digit is 5.

Hence, 4335 is not divisible by 6.

(d) 61233

The number is not divisible by 2 as the last digit is 3.

Hence, 61233 is not divisible by 6.

(e) 901352

The number is divisible by 2 as the last digit is 2.

The sum of digits is $9+0+1+3+5+2 = 20$, which is not divisible by 3.

Hence, 901352 is not divisible by 6.

(f) 438750

The number is divisible by 2 as the last digit is 0.

The sum of digits is $4+3+8+7+5+0 = 27$, which is divisible by 3.

Hence, 438750 is divisible by 6.

(g) 1790184

The number is divisible by 2 as the last digit is 4.

The sum of digits is $1+7+9+0+1+8+4 = 30$, which is divisible by 3.

Hence, 1790184 is divisible by 6.

(h) 12583

The number is not divisible by 2 as the last digit is 3.

Hence, 12583 is not divisible by 6.

(i) 639210

The number is divisible by 2 as the last digit is 0.

The sum of digits is $6+3+9+2+1+0 = 21$, which is divisible by 3.

Hence, 639210 is divisible by 6.

(j) 17852

The number is divisible by 2 as the last digit is 2.

The sum of digits is $1+7+8+5+2 = 23$, which not is divisible by 3.

Hence, 17852 is not divisible by 6.

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