Why are 39 and 4 congruent modulo 7?

In number theory, two integers are considered congruent modulo $N$ if their difference is evenly divisible by $N$.12

To determine why 39 and 4 are congruent modulo 7, you calculate the difference between the two numbers:
$$39-4=35$$

Because 35 is evenly divisible by 7 ($35÷7=5$), the condition for congruence is satisfied. Therefore, 39 and 4 belong to the same congruence class modulo 7, expressed as:
$$39\equiv 4\left(\mathrm{mod}7\right)$$