# Prime factors

The five prime numbers 3, 7, 11, 13 and 37 are special. When they are multiplied together, the result is 111 111.

3 x 7 x 11 x 13 x 37 =111111 What is the product of 23 and these five prime numbers? Five of the digits are the same. Why is this?

SOLUTIONS District nurse (ages 8 to 13). 1 Possible routes for a single visit to each town are ABCDA (or reverse), ABDCA (or reverse) or ACBDA (or reverse). The shortest route is 40 miles. 2 For the week of January, possible routes are ACDBCA (or reverse), which is 53 miles long; or ABCBCA (or reverse) or ADCBCA (or reverse), each of which is 51 miles long. Prime factors (ages 11 to 14) 23 x 111 111 = 2 555 553, because 2 + 3 = 5.

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