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There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. The total number of sections thus formed are:
- a)22
- b)16
- c)36
- d)21
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are 576 boys and 448 girls in a school that are to be divided in...
The number 576 can be factorised as,
576 = 2×2×2×2×2×2×3×3
The number 448 can be factorised as,
448=2×2×2×2×2×2×7
Write the common factors of the given numbers.
2×2×2×2×2×22×2×2×2×2×2
Multiply the common factors to determine the highest common factor (HCF) of the given numbers.
2×2×2×2×2×2 = 642×2×2×2×2×2 = 64
Since the highest common factor (HCF) of the given numbers is 64, this implies that each section will have 64 number of students.
Now, we need to find the number of sections formed.
Let us first find the number of sections formed by the total number of boys by dividing 576 by 64.
576/64 = 9
Now, find the number of sections formed by the total number of girls by dividing 448 by 64.
448/64=7
Thus, the total number of sections formed will be 9+7=16
Hence, option B is the correct answer.
576 = 2×2×2×2×2×2×3×3
The number 448 can be factorised as,
448=2×2×2×2×2×2×7
Write the common factors of the given numbers.
2×2×2×2×2×22×2×2×2×2×2
Multiply the common factors to determine the highest common factor (HCF) of the given numbers.
2×2×2×2×2×2 = 642×2×2×2×2×2 = 64
Since the highest common factor (HCF) of the given numbers is 64, this implies that each section will have 64 number of students.
Now, we need to find the number of sections formed.
Let us first find the number of sections formed by the total number of boys by dividing 576 by 64.
576/64 = 9
Now, find the number of sections formed by the total number of girls by dividing 448 by 64.
448/64=7
Thus, the total number of sections formed will be 9+7=16
Hence, option B is the correct answer.
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There are 576 boys and 448 girls in a school that are to be divided in...
To find the total number of sections that can be formed, we need to divide the total number of students by the number of students in each section.
Given:
Number of boys = 576
Number of girls = 448
Let's assume the number of students in each section is x.
We can divide the total number of boys by x to find the number of sections of boys and the total number of girls by x to find the number of sections of girls.
Number of sections of boys = 576 / x
Number of sections of girls = 448 / x
Since we need to divide the students into equal sections of either boys or girls alone, the number of sections of boys and girls should be integers.
So, the value of x should be a common factor of both 576 and 448.
Finding the common factors of 576 and 448:
The prime factorization of 576:
576 = 2^6 * 3^2
The prime factorization of 448:
448 = 2^6 * 7
The common factors of 576 and 448 are powers of 2. The highest power of 2 that divides both numbers is 2^6.
So, x = 2^6 = 64.
Number of sections of boys = 576 / 64 = 9
Number of sections of girls = 448 / 64 = 7
Total number of sections = Number of sections of boys + Number of sections of girls
Total number of sections = 9 + 7 = 16
Therefore, the correct answer is option B) 16.
Given:
Number of boys = 576
Number of girls = 448
Let's assume the number of students in each section is x.
We can divide the total number of boys by x to find the number of sections of boys and the total number of girls by x to find the number of sections of girls.
Number of sections of boys = 576 / x
Number of sections of girls = 448 / x
Since we need to divide the students into equal sections of either boys or girls alone, the number of sections of boys and girls should be integers.
So, the value of x should be a common factor of both 576 and 448.
Finding the common factors of 576 and 448:
The prime factorization of 576:
576 = 2^6 * 3^2
The prime factorization of 448:
448 = 2^6 * 7
The common factors of 576 and 448 are powers of 2. The highest power of 2 that divides both numbers is 2^6.
So, x = 2^6 = 64.
Number of sections of boys = 576 / 64 = 9
Number of sections of girls = 448 / 64 = 7
Total number of sections = Number of sections of boys + Number of sections of girls
Total number of sections = 9 + 7 = 16
Therefore, the correct answer is option B) 16.
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