Question

A shopkeeper has 3 packets that can have 294, 252 or 210 items. Each packet has sections
holding the same number of items. What is the greatest number of items that can be put
in a section?​

Answer 1

294 = 2 × 3 × 7^2

252 = 2^2 × 3^2 × 7

210 = 2 × 3 × 5 × 7

HCF = 2 × 3 × 7

HCF = 42 students

Answer 2

Answer: The greatest number of items that can be put

in a section is 42 items.

Step-by-step explanation

• To find the greatest no of items we will find out HCF.
• HCF is defined as the highest factor that divides the given numbers

• Factors of 294 are  given as

      $294 = 2 * 3 * 7^2$

• Factors of 252 are  given as

      $252 = 2^2 * 3^2 * 7$

• Factors of 210 are  given as

      $210 = 2 * 3 * 5 * 7$

• The HCF of 294,252,210 is given by

       $HCF = 2 * 3 * 7\\HCF=42$

Conclusion:

The greatest number of items that can be put in a section is 42 items.