if A679B is a five digit number is divisible by 72 find A and B
Answers
Given, A679B a number.
Need to find out it is divisible by 72.
⇒ Prime factors of 72 = 9 and 8
So, it is enough to check the given 5-digit number is divisible by 9 and 8.
⇒ To check the number is divisible by 8 last three digits must be divisible by 8.
⇒ 79B is divisible by 8 should be checked.
⇒ Now, from divisibility rule 100b + 10c + d
We get
⇒ 100(7) + 10(9) + B = 790 + B
Substitute a number in B which satisfy the equation using trail error method
⇒ B must be 2 to be divisible by 8
⇒ 792 is divisible by 8
∴ A679B = A6792 is divisible by 8
⇒ A6792 is divisible by 9 only if sum of the given digits is divisible by 9
⇒ A + 6 + 7 + 9 + 2 = A + 24
Put a value in A which satisfy the equation
A = 3
A + 24 = 27 is divisible by 9.
∴ A679B is divisible by 72 and the values of A = 3 and B = 2
Hence, 36792 is divisible by 72
Answer:
a=2, b=3
Step-by-step explanation:
If a number is divisible by 72 then,
It is definitely divisible by 8 and 9.
Divisibility by 8:
The last three digits should be divisible by 8.
Check the last three digits it is 79b.
79b must be divisible by 8.
2 is the value of b.
Divisibility by 9:
The Sum of all digits must be equal to 9 or a multiple of 9.
Check the number it is a679b where b is 2, so we can say the number is a6792.
a6792 must be divisible by 9. 3 is the value of a.
Therefore a+b=5.
a=2, b=3
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