Calcula y contesta.
14. ¿Es 7 divisor de 70? ¿Y de 75?
15. ¿Es 6 divisor de 102? ¿Y de 114?
Answer (2)
7 is a divisor of 70 but not of 75. 6 is a divisor of both 102 and 114.
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Check if 7 is a divisor of 70: 7 70 = 10 , which is an integer.
Check if 7 is a divisor of 75: 7 75 ≈ 10.71 , which is not an integer.
Check if 6 is a divisor of 102: 6 102 = 17 , which is an integer.
Check if 6 is a divisor of 114: 6 114 = 19 , which is an integer.
7 is a divisor of 70, 6 is a divisor of 102 and 114, 7 is not a divisor of 75.
Explanation
Problem Analysis We need to determine if 7 is a divisor of 70 and 75, and if 6 is a divisor of 102 and 114. A number 'a' is a divisor of 'b' if b/a is an integer.
Checking if 7 is a divisor of 70 First, let's check if 7 is a divisor of 70. We divide 70 by 7: 707 = 10
Since 10 is an integer, 7 is a divisor of 70.
Checking if 7 is a divisor of 75 Next, let's check if 7 is a divisor of 75. We divide 75 by 7: 757 ≈ 10.71
Since 10.71 is not an integer, 7 is not a divisor of 75.
Checking if 6 is a divisor of 102 Now, let's check if 6 is a divisor of 102. We divide 102 by 6: 1026 = 17
Since 17 is an integer, 6 is a divisor of 102.
Checking if 6 is a divisor of 114 Finally, let's check if 6 is a divisor of 114. We divide 114 by 6: 1146 = 19
Since 19 is an integer, 6 is a divisor of 114.
Final Answer Therefore, 7 is a divisor of 70, but not of 75. 6 is a divisor of both 102 and 114.
Examples
Understanding divisibility is crucial in many real-life scenarios. For instance, if you're dividing a batch of cookies among friends, you need to know if the number of cookies is divisible by the number of friends to ensure everyone gets an equal share. Similarly, in scheduling tasks, knowing if the total time required is divisible by the number of workers helps in distributing the workload evenly. These basic division principles are fundamental in resource allocation and planning.
