To calculate 17x26 without using the 7 button, you could break down the numbers using addition and multiplication. First, express 26 as 20 + 6, then calculate 17x20 and 17x6 separately. Finally, add the two results together: (17 \times 20 = 340) and (17 \times 6 = 102), so (340 + 102 = 442). Thus, 17x26 equals 442.