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Mathematics Question on Tests for Divisibility of Numbers

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

(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.