How many digits does gcd(111...111, 111...111) have?
The first number has 240 ones and the second number has 150 ones.
111111111111 (twelve ones)
111111111111 /11= 101010101
111111111111 /111 = 1001001001
111111111111 /1111= 100010001
111111111111 /111111= 1000001
It seems that: a number composed by n digits "one" is divisible by any other number composed by m digits "one" if, and only if, m is a divisor of n.
In our case we have two numbers n1 and n2 with 240 and 150 digits.
240 (n1) is divisible by (2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120)
150 (n2) is divisible by (2, 3, 5, 6,10, 15, 25, 30, 50, 75)
gdc=30
Edited on March 6, 2019, 4:41 pm
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Posted by armando
on 2019-03-06 12:12:43 |
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