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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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