Question

Using divisibility tests, determine which of following numbers are divisible by 6:

1. 297144
2. 1258
3. 4335
4. 61233
5. 901352
6. 438750
7. 1790184
8. 12583
9. 639210
10. 17852

Answer 1

(a) 297144
\(→\) Divisible by 2 as its units place is an even number.
\(→\)Divisible by 3 as sum of its digits (= 27) is divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is also divisible by 6.

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(b) 1258
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Not divisible by 3 as sum of its digits (= 16) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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(c) 4335
\(→\) Not divisible by 2 as its units place is not an even number.
\(→\)Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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(d) 61233
\(→\) Not divisible by 2 as its units place is not an even number.
\(→\) Divisible by 3 as sum of its digits (= 15) is divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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(e) 901352
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Not divisible by 3 as sum of its digits (= 20) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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(f) 438750
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Divisible by 3 as sum of its digits (= 27) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

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(g) 1790184
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Divisible by 3 as sum of its digits (= 30) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

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(h) 12583
\(→\) Not divisible by 2 as its units place is not an even number.
\(→\) Not divisible by 3 as sum of its digits (= 19) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.

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(i) 639210
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Divisible by 3 as sum of its digits (= 21) is not divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.

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(j) 17852
\(→\) Divisible by 2 as its units place is an even number.
\(→\) Not divisible by 3 as sum of its digits (= 23) is not divisible by 3.
Since the number is not divisible by both 2 and 3, therefore, it is not divisible by 6.