The greatest number that satisfies the given conditions is 2.
Let's call the greatest number that divides 148 and 246 and leaves remainders of 4 and 6, respectively, as "n".
This means that there exist integers "a" and "b" such that:
148 = an + 4 246 = bn + 6
We can rewrite these equations as:
an = 148 - 4 = 144 bn = 246 - 6 = 240
To find the greatest common divisor (GCD) of 144 and 240, we can use the Euclidean algorithm:
240 = 1 * 144 + 96 144 = 1 * 96 + 48 96 = 2 * 48 + 0
Therefore, the GCD of 144 and 240 is 48.
Since n divides both 144 and 240, it must also divide their GCD, which is 48. Therefore, the greatest number that will divide 148 and 246 leaving remainders of 4 and 6, respectively, is n = 48.