Among how many children may 429 mangoes and also 715 oranges be equally divided ?

Options

A. 143
B. 15
C. 18
D. 153

Answer

To determine among how many children 429 mangoes and 715 oranges can be equally divided, we need to find the greatest common divisor (GCD) of the two numbers. Here’s the step-by-step solution:

### Step 1: Prime Factorization
First, we will perform the prime factorization of both numbers.

**For 429:**
- Divide by 3: \( 429 ÷ 3 = 143 \)
- Now, factor 143: \( 143 ÷ 11 = 13 \)
- Thus, the prime factorization of 429 is:
\[ 429 = 3 \times 11 \times 13 \]

**For 715:**
- Divide by 5: \( 715 ÷ 5 = 143 \)
- Now, factor 143: \( 143 ÷ 11 = 13 \)
- Thus, the prime factorization of 715 is:
\[ 715 = 5 \times 11 \times 13 \]

### Step 2: Identify Common Factors
Next, we identify the common factors from the prime factorizations of both numbers:
- The common factors are \( 11 \) and \( 13 \).

### Step 3: Calculate the GCD
To find the GCD, we multiply the common prime factors:
\[ GCD = 11 \times 13 = 143 \]

### Step 4: Conclusion
Therefore, the number of children among whom 429 mangoes and 715 oranges can be equally divided is **143**.