Question

Using divisibility test, 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

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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.

(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.