Question

Write the greatest 6 digit number and find its prime factors.​

Answer 1

Step-by-step explanation:

ababab in decimal system is 105a+104b+103a+102b+10a+b=10101(10a+b)=10101×(ab)10

It is known that ababab is a product of 6 distinct primes.

Also, 10101=3×7×13×37

Thus, (ab)10 has to be expressed as a product of 2 prime numbers, none of them from {3,7,13,37}

Such possible prime pairs are (2,5),(2,11),(2,17),(2,19),(2,23),(2,29),(2,31),(2,41),(2,43),(2,47),(5,11),(5,17),(5,19)

A total of 13 such numbers are possible.

Answer 2

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