Did you notice in Table 5.1 that no rule for 7 was given? Here is a rule for determining if counting number n is divisible by 7. Any number has a units digit (it may be 0), a tens digit, a hundreds digit, and so forth. To see if n is divisible by 7, separate n into a units digit, u_n, and all the digits to the left of u_n, 10r_n. Then the test for divisibility by 7 is

a. 364

b. 1,283

c. 251,895

d. 627,746

Table 5.1

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7 (r2u,) if and only if 7 n For example, we see that 7 divides 616 because 61 - 2(6) = 49 and 7 divides 49. Decide whether 7 divides each of the given numbers.