This question tests middle school quantitative reasoning skills: understanding and applying divisibility and factors. Divisibility means a number can be divided by another number without leaving a remainder. Factors are numbers you can multiply to get another number. In this problem, the scenario involves finding the missing factor in 9 × __ = 72, requiring understanding of inverse operations. The correct answer, choice B (8), is correct because 9 × 8 = 72, making 8 the missing factor. This can be found by dividing: 72 ÷ 9 = 8. Choice C (9) would give 9 × 9 = 81, not 72. To help students: Encourage using division to find missing factors (72 ÷ 9 = ?). Teach checking answers by multiplying back. Emphasize the relationship between multiplication and division as inverse operations.

This question tests middle school quantitative reasoning skills: understanding and applying divisibility and factors. Divisibility means a number can be divided by another number without leaving a remainder. Factors are numbers you can multiply to get another number. In this problem, the scenario involves finding the greatest common factor (GCF) of 60 cookies and 36, requiring understanding of common factors. The correct answer, choice B (12), is correct because the factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60} and the factors of 36 are {1,2,3,4,6,9,12,18,36}, with 12 being the largest number in both lists. Choice C (18) is incorrect because while 18 is a factor of 36, it is not a factor of 60 (60 ÷ 18 = 3.33...). To help students: Encourage listing all factors of each number systematically. Teach identifying common factors by finding numbers in both lists. Emphasize that the GCF is the largest of the common factors.

This question tests middle school quantitative reasoning skills: understanding and applying divisibility and factors. Divisibility means a number can be divided by another number without leaving a remainder. Factors are numbers you can multiply to get another number. In this problem, the scenario involves identifying the complete set of factors of 60 cookies, requiring systematic factor finding. The correct answer, choice A, is correct because it lists all factors of 60: 1×60, 2×30, 3×20, 4×15, 5×12, and 6×10 are all the factor pairs. Choice B incorrectly includes 7, which is not a factor (60 ÷ 7 = 8.57...). To help students: Encourage finding factors in pairs starting from 1. Teach checking completeness by verifying each number divides 60 evenly. Emphasize that the list should include all numbers from 1 up to the square root, plus their pairs.

This question tests middle school quantitative reasoning skills: understanding and applying divisibility and factors. Divisibility means a number can be divided by another number without leaving a remainder. Factors are numbers you can multiply to get another number. In this problem, the scenario involves identifying which number is a factor of 36 chairs, requiring understanding of what makes a number a factor. The correct answer, choice B (6), is correct because 6 × 6 = 36, making 6 a factor of 36. Choice A (7) is incorrect because 36 ÷ 7 = 5.14..., which is not a whole number, so 7 is not a factor of 36. To help students: Encourage practice with factor pairs (1×36, 2×18, 3×12, 4×9, 6×6). Teach systematic checking by dividing to see if you get whole numbers. Emphasize that factors always divide evenly into the original number.

This question tests middle school quantitative reasoning skills: understanding and applying divisibility and factors. Divisibility means a number can be divided by another number without leaving a remainder. Factors are numbers you can multiply to get another number. In this problem, the scenario involves identifying which number is NOT a factor of 36 chairs, requiring understanding of factor relationships. The correct answer, choice D (8), is correct because 36 ÷ 8 = 4.5, which is not a whole number, meaning 8 is not a factor of 36. Choices A (9), B (3), and C (4) are all factors of 36 because 36 ÷ 9 = 4, 36 ÷ 3 = 12, and 36 ÷ 4 = 9, all giving whole number results. To help students: Encourage listing all factor pairs systematically. Teach checking each option by division. Emphasize that non-whole quotients indicate non-factors.