19. Next year's 'leap day', 29th February 2024 , may be written in 'ddmmyy' format as the number 290224. What is the sum of all the two-digit factors of 290224 ?
Solution
397

The prime factorisation of 290224 is $290224=2 \times 2 \times 2 \times 2 \times 11 \times 17 \times 97$.
Since the product of any two of $11,16=2^{4}, 17$ and 97 will not be a two-digit number, we need only consider 16 ; as well as $11,17,97$ and any multiples of each of these by the powers of two. The only such two-digit multiples are $22,44,88 ; 34,68$.
The sum of these numbers is $11+16+17+97+22+44+88+34+68=397$.