4. 24 and 96\nhow many factors do the numbers have in common?\n5. 28 and 21\n6. 20 and 90\nexplain how you…

4. 24 and 96\nhow many factors do the numbers have in common?\n5. 28 and 21\n6. 20 and 90\nexplain how you found the gcf.\n7. 66 and 121\nhow many factors do the numbers have in common?

4. 24 and 96\nhow many factors do the numbers have in common?\n5. 28 and 21\n6. 20 and 90\nexplain how you found the gcf.\n7. 66 and 121\nhow many factors do the numbers have in common?

Answer

Explanation:

Step1: Prime - factorize the numbers

For (24 = 2\times2\times2\times3) and (96=2\times2\times2\times2\times2\times3). The common prime - factors are (2\times2\times2\times3 = 24). The factors of (24) are (1,2,3,4,6,8,12,24), so there are 8 common factors.

Step2: Prime - factorize 28 and 21

(28 = 2\times2\times7) and (21=3\times7). The common factor is 7, so there is 1 common factor.

Step3: Prime - factorize 20 and 90

(20 = 2\times2\times5) and (90=2\times3\times3\times5). The GCF is (2\times5 = 10). We found the GCF by first listing the prime factors of each number. Then we identified the common prime factors. The GCF is the product of the lowest - power of each common prime factor. Here, the common prime factors are 2 and 5, and we take the lowest power of 2 (which is (2^1)) and 5 (which is (5^1)) and multiply them ((2\times5 = 10)).

Step4: Prime - factorize 66 and 121

(66 = 2\times3\times11) and (121 = 11\times11). The common factor is 11, so there is 1 common factor.

Answer:

  1. 8
  2. 1
  3. The GCF of 20 and 90 is 10. We found it by prime - factorizing the numbers ((20 = 2\times2\times5) and (90=2\times3\times3\times5)), identifying the common prime factors (2 and 5), and multiplying the lowest - power of each common prime factor ((2\times5 = 10)).
  4. 1