In long division for 1/7, the possible non-zero remainders are 1, 2, 3, 4, 5, 6 (six values). The decimal of 1/7 therefore:

At each step in long division by 7, only six non-zero remainders are possible. By the pigeonhole principle, within 7 steps a remainder must repeat — and once it does, the digit sequence loops. So 1/7 must terminate or repeat within at most 6 steps. In fact 1/7 = 0.142857142857… has a 6-digit repeating block — exactly matching the maximum possible cycle length.