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Question

Difficulty: EasyFactors, Multiples, and Primes

Determine the total number of positive factors for each of the following integers. Then, place the integers in order from the one with the fewest factors to the one with the most factors.

  1. 1The integer 77
  2. 2The integer 99
  3. 3The integer 88
  4. 4The integer 1212

Answer

The correct sequence is: The integer 77 (2 factors), The integer 99 (3 factors), The integer 88 (4 factors), and The integer 1212 (6 factors).
By counting the positive divisors of each number, we find that 77 has two factors, 99 has three factors, 88 has four factors, and 1212 has six factors. Placing them in ascending order of their factor counts yields 7,9,87, 9, 8, and 1212.

Step-by-Step Solution

1
List all positive factors for the integer 1212.
The factors of 1212 are 1,2,3,4,61, 2, 3, 4, 6, and 1212. There are 66 factors in total.
Finding the total count of factors is required to compare and order the integers.
2
List all positive factors for the integer 77.
The factors of 77 are 11 and 77. There are 22 factors in total.
Determining the factor count for each number allows for proper sorting.
3
List all positive factors for the integer 88.
The factors of 88 are 1,2,41, 2, 4, and 88. There are 44 factors in total.
We must evaluate every integer provided in the list.
4
List all positive factors for the integer 99.
The factors of 99 are 1,31, 3, and 99. There are 33 factors in total.
This completes the factor counting for all items.
5
Sort the integers based on their factor counts from fewest to most.
The sequence is 22 factors (The integer 77), then 33 factors (The integer 99), then 44 factors (The integer 88), and finally 66 factors (The integer 1212).
The question asks to place the integers in order from fewest factors to most factors.

Key Concept

Factors and Prime Numbers
Estimated Time:45s
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Topics

Factors, Multiples, and Primes

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