1.

Find the cardinality of a set x=(x:x is a composite factor of 1020​

Answer»

Given:

Set X such that, X = (X : X is a composite factor of 1020​)

To find:

Cardinality

Solution:

  • We know that factors of 1020 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020
  • Composite numbers are the numbers that are divisible by more than just 1 and itself.
  • Thus, the composite factor of 1020​ are = 4, 6, 10, 12, 15, 20, 30, 34, 51, 60, 68, 85, 102, 170, 204, 255, 340, 510, 1020
  • Since the composite factors are 19 in total.
  • Therefore, the cardinality of set X is 19.


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