Consider all 6-digit numbers of the form of abccba where b is odd. Determine the 6-digit numbers that are divisible by 7.
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Answer:
Short answer is 70
How?
The structure of the number abccba is palindrome
Palindromes are divisible by 11
Our number is
10000a + 10000b + 1000c + 100c + 10b + a
On grouping like terms, we get
100001a + 10010b + 1100c
On dividing by 11 the number is reduced to
9091a + 910b + 100c, which cab be expressed as
9093a-2a + 130x7b + 98c + 2c
--> 1299x7a +130x7b +14x7c -2(a-c)
For the above to be divisible by 7,
Step-by-step explanation:
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