Answer:
100 has more divisors than 55.
Step-by-step explanation:
The prime factorization of 100 is ...
... 100 = 2²×5²
The number of divisors of 100 is the product of the exponents of these factors, after each has been increased by 1: (2+1)(2+1) = 9. Those divisors are ...
... 1, 2, 4, 5, 10, 20, 25, 50, 100
A rectangle can be formed with each divisor as the length of a side. If we count 1×100 and 100×1 as the same rectangle, then 5 different rectangles are possible:
... 1×100, 2×50, 4×25, 5×20, 10×10
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On the other hand, the prime factorization of 55 is ...
... 55 = 5¹×11¹
This means the number of divisors is (1+1)(1+1) = 4. Those divisors are ...
... 1, 5, 11, 55
The number of rectangles that can be formed from these is 2:
... 1×55, 5×11
100 has more divisors, so there are more ways that rectangles can be formed from them.
