Quick Times
$32 \times 38 = 30 \times 40 + 2 \times 8$
$34 \times 36 = 30 \times 40 + 4 \times 6$
$56 \times 54 = 50 \times 60 + 6 \times 4$
$73 \times77 = 70 \times80 + 3 \times 7$
And so on?
Verify and generalise if possible.
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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
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