Mathematics
A number is divisible by both 3 and 8. By which other numbers will that number be always divisible?
Answer
Let a natural number, say n, be divisible by both 3 and 8.
Since 3 and 8 are co-prime numbers and if a number is divisible by two co-prime numbers, then it is divisible by their product.
So, n is divisible by 3 × 8 = 24.
We know that,
If a number is divisible by another number, then it is divisible by each of the factors of that number
Thus, n is divisible by all the factors of 24.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Hence, the number is always divisible by 1, 2, 4, 6, 12 and 24.
Related Questions
Determine if 372645 is divisible by 45.
A number is divisible by 12. By what other numbers will that number be divisible?
State whether the following statements are true (T) or false (F):
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 3, it must be divisible by 9.
(iii) If a number is divisible by 9, it must be divisible by 3.
(iv) If a number is divisible by 9 and 10 both, it must be divisible by 90.
(v) If a number divides the sum of two numbers, then it must divide the two numbers separately.
(vi) If a number is divisible by 3 and 8 both, it must be divisible by 12.
(vii) If a number is divisible by 6 and 15 both, it must be divisible by 90.
Here are two different factor trees of the number 90. Write the missing numbers:
