Answer:
The greatest number is 11
Step-by-step explanation:
Given
Dividends: 181 and 236
Remainder: 5
Required
Determine a divisor that satisfies the above condition
Let the required divisor be represented with x.
Since a remainder of 5 is expected, then x can divide (181 - 5) and (236 - 5) without remainders.
So, we have:
[tex]181 - 5 = 176[/tex]
[tex]236 - 5 = 231[/tex]
Next, we calculate the GCF of 176 and 231
[tex]176 = 2 * 2 * 2 * 2 * 11[/tex]
[tex]231 = 3 * 7 * 11[/tex]
The greatest common factor, GCT is:
[tex]GCF = 11[/tex]
Hence, the required divisor is 11
