(Sum of multiples of 7 between 21 and 49) `div` (Biggest common factor of 25 and 30) is equal to

Options

A. 35
B. 37
C. 14
D. 21

Answer

To solve the question, we need to follow these steps:

### Step 1: Find the multiples of 7 between 21 and 49.
The multiples of 7 in this range are:
- 21 (7 x 3)
- 28 (7 x 4)
- 35 (7 x 5)
- 42 (7 x 6)
- 49 (7 x 7)

However, since we are looking for multiples strictly between 21 and 49, we will consider:
- 28
- 35
- 42

### Step 2: Calculate the sum of these multiples.
Now, we add these multiples together:
\[ 28 + 35 + 42 \]
Calculating this step-by-step:
- First, add 28 and 35:
\[ 28 + 35 = 63 \]
- Now, add 42 to the result:
\[ 63 + 42 = 105 \]

So, the sum of the multiples of 7 between 21 and 49 is 105.

### Step 3: Find the biggest common factor (HCF) of 25 and 30.
To find the HCF, we can list the factors of each number:
- Factors of 25: 1, 5, 25
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

The common factors are:
- 1 and 5

The biggest common factor is 5.

### Step 4: Divide the sum of the multiples by the HCF.
Now, we divide the sum of the multiples (105) by the HCF (5):
\[ 105 \div 5 \]
Calculating this gives:
\[ 105 \div 5 = 21 \]

### Final Answer:
Thus, the final answer to the question is 21.

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