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266 cola cans and 322fr fruit juice cans need to be stacked in a school canteen if each stack is of same height and is to contain cans of same type, the greatest number of cans each stack can have is
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266 cola cans and 322fr fruit juice cans need to be stacked in a schoo...
Problem:

266 cola cans and 322 fruit juice cans need to be stacked in a school canteen if each stack is of same height and is to contain cans of same type, the greatest number of cans each stack can have is:


Solution:

To find the greatest number of cans each stack can have, we need to find the highest common factor (HCF) of the given numbers.


Step 1: Prime factorization

Write the given numbers as products of prime factors.



  • 266 = 2 x 7 x 19

  • 322 = 2 x 7 x 23



Step 2: Identify common factors

Identify the prime factors that are common to both numbers.



  • Common factors = 2 x 7 = 14



Step 3: Find HCF

Multiply the common factors to find the HCF.



  • HCF = 14



Step 4: Calculate the number of cans each stack can have

Divide each given number by the HCF to find the greatest number of cans each stack can have.



  • Greatest number of cola cans in each stack = 266 ÷ 14 = 19

  • Greatest number of fruit juice cans in each stack = 322 ÷ 14 = 23



Step 5: Check the answer

Verify that the number of cans in each stack is a whole number and that the stacks are of the same height.



  • 19 x 14 = 266

  • 23 x 14 = 322



Final answer:

The greatest number of cans each stack can have is 14. Each stack can have 19 cola cans or 23 fruit juice cans.
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266 cola cans and 322fr fruit juice cans need to be stacked in a school canteen if each stack is of same height and is to contain cans of same type, the greatest number of cans each stack can have is
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