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.
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.