1. Which of the following is the set of common factors of 36 and 54?
A. 1,3,4,6,9
B. 1,2,3,4,6
C. 1,2,3,6,9
D. 1,2,3,4,9
2. How many whole numbers between 155 and 232 is divisible by 2, 5, and 10?
A. 7
B. 5
C. 6
D. 8
3. How many whole numbers between 50 and 120 are divisible by 3, 6 and 9?
A. 3
B. 4
C. 5
D. 6
4. Which set is the common factor of 66 and 110?
A. 2 and 3
B. 3 and 5
C. 2 and 11
D. 5 and 11
5. By what numbers is 2 310 divisible?
A. 7 and 9
B. 9 and 10
C. 7 and 11
D. 9 and 11
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Answers & Comments
Verified answer
Factors, Multiples, and Divisibility Rules
Factors are numbers that when multiplied will result to the given number. It divides that number without leaving any remainder. Multiples are the products of multiplying a certain number by 1 - 10. Divisibility rules are set of specific rules that apply to a number to check whether the given number is divisible by a particular number or not. Helps find the factors and multiples of numbers without performing long division.
Answers:
Solutions:
1. Factors of 36 and 54.
36 - 1, 2, 3, 4, 6, 9, 18, 36
54 - 1, 2, 3, 6, 9, 18, 27, 54
Common Factors: 1, 2, 3, 6, 9
2. Divisible by 2, 5, and 10 between 155 and 232.
Applying the rule for divisibility by 2, 5, and 10 we get
160, 170, 180, 190, 200, 210, 220, and 230 = 8
Therefore, there are 8 numbers between 155 and 232 that are divisible by 2, 5, and 10.
3. Divisible by 3, 6, and 9 between 50 and 120.
3 - 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105,
108, 111, 114, 117, 120
6 - 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120
9 - 54, 63, 72, 81, 90, 99, 108, 117
Common Multiples: 54, 72, 108 = 3
Therefore, there are 3 numbers between 50 and 120 that are divisible by 3, 6, and 9.
4. Common Factor of 66 and 110
66 - 1, 2, 3, 6, 11
110 - 1, 2, 5, 10, 11
Common Factors: 1, 2, 11
5. Numbers by which 2310 is divisible.
2310 ÷ 7 = 330
2310 ÷ 9 = 256 r. 6
2310 ÷ 10 = 231
2310 ÷ 11 = 210
Therefore, 2310 is divisible by 7, 10, and 11 but not with 9.
What are factors: brainly.ph/question/7246389
What are multiples: brainly.ph/question/9855945
What are divisibility rules: brainly.ph/question/6111965
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