To find the largest number of students who can share 42 pens and 70 pencils equally, we need to find the greatest common divisor (GCD) of 42 and 70.

Step 1: Find the prime factorizations of 42 and 70.

• 42 = 2 × 3 × 7
• 70 = 2 × 5 × 7

Step 2: Identify the common factors.

The common factors between 42 and 70 are 2 and 7.

Step 3: Multiply the common factors.

The GCD is $2 \times 7 = 14$.

Step 4: Conclusion

The largest number of students who can share the pens and pencils equally is 14. Each student would receive:

• $\frac{42}{14} = 3$ pens
• $\frac{70}{14} = 5$ pencils

Would you like further details or have additional questions?

Related questions:

1. How would the answer change if the total number of pens and pencils were different?
2. How do you calculate the GCD of two numbers using the Euclidean algorithm?
3. Can you apply the same approach to more than two numbers?
4. What is the least common multiple (LCM) of 42 and 70?
5. How do you calculate the number of ways to distribute the pens and pencils equally among students?

Tip: To find the GCD, break each number down into its prime factors and look for the highest number of common prime factors.