Final answer:
The correct answer is option b) 6, found by comparing the prime factors of N and 66 and choosing the largest number that is a factor of both, which is 6 (2×3).
Step-by-step explanation:
The correct answer is option b) 6.
To find the greatest common factor (GCF) of the number N and 66, we need to look at the prime factorization of both numbers. We know the prime factorization of 66 is 2×3×3 (or 2×32), because 66 equals 2 times 33. We are given that the GCF of the number N and 2×3×3×5 is already determined as a number on the list. The only number that is common to both sets of prime factors (the given one for N and 2×3×3 for 66) without considering the 5 (as it is not a prime factor of 66) is 6, represented by the prime factors 2×3. Therefore, the number common to both N and 66, which would be their GCF, is 6.
To find the greatest common factor (GCF) of the number N and 66, we need to compare their prime factorizations. The prime factorization of N is given as 2•3•3•5.
The prime factorization of 66 is 2•3•11.
To find the GCF, we take the product of the common prime factors, each raised to the smaller power. In this case, both numbers have 2 and 3 as common factors. So, the GCF is 2•3 = 6.