If a number is both a factor of 36 and a multiple of 6, which of the following i

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Question: If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?

Options:

Correct Answer: 18

Solution:

The factors of 36 that are also multiples of 6 are 6, 12, and 18. Among these, 18 is the largest.

If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?

If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?

Step 1: Identify the factors of 36. Factors are numbers that can divide 36 without leaving a remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: Identify the multiples of 6. Multiples of 6 are numbers that can be obtained by multiplying 6 by whole numbers (0, 1, 2, 3, ...). The first few multiples of 6 are 6, 12, 18, 24, 30, 36, ...
Step 3: Find the common numbers between the factors of 36 and the multiples of 6. From the factors of 36 (1, 2, 3, 4, 6, 9, 12, 18, 36) and the multiples of 6 (6, 12, 18, 24, 30, 36), the common numbers are 6, 12, and 18.
Step 4: Determine the largest number from the common numbers found in Step 3. The common numbers are 6, 12, and 18, and the largest of these is 18.

Factors and Multiples – Understanding the relationship between factors (numbers that divide evenly into another number) and multiples (numbers that can be obtained by multiplying a number by an integer).
Divisibility Rules – Applying rules to determine if a number is a multiple of another, particularly focusing on the number 6 in this case.
Set Intersection – Finding common elements between two sets: factors of 36 and multiples of 6.