Question

TWO INTEGERS ARE DEFINED AS "PARTNERS" IF BOTH OF THEIR PRIME FACTORIZATIONS CONTAIN ALL THE SAME PRIME FACTORS. FOR EXAMPLE, 15 AND 45 ARE PARTNERS SINCE BOTH ARE DIVISIBLE BY THE SAME SET OF PRIME NUMBERS 3 AND 5. HOW MANY POSITIVE INTEGERS GREATER THAN 50 AND LESS THAN 100 HAVE ATLEAST ONE PARTNER GREATER THAN 50 AND LESS THAN 100?

Answer 1

partner pairs (and their factors)

54 and 72 (2 3)
54 and 96 (2 3)
56 and 98 (2 7)
60 and 90 (2 3 5)
72 and 96 (2 3)