Prime factorization

• Prime factorization of 399: 399 = 3¹×7¹×19¹
• Prime factorization of 532: 532 = 2²×7¹×19¹

Common factors:

• 3 (from 399)
• 7 (from both 399 and 532)
• 19 (from both 399 and 532)
• 1 (considered as a factor)

So, the common factors are 3, 7, 19, and 1, which are 4 different bottle sizes.

Therefore, the correct answer is: (b) 4.    

Approach 2:

• To find the different bottle sizes possible, we need to determine the common factors of 399 and 532 because each bottle size must evenly divide the amount of petrol or diesel in their respective cans.
• Let's find the factors of 399 and 532:
  
  
• Factors of 399: 1, 3, 7, 19, 21, 57, 133, 399 
• Factors of 532: 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532
• The common factors of 399 and 532 are 1, 7, 19 and 133. These represent the possible bottle sizes in terms of litres that can evenly divide the amounts of petrol and diesel in the cans.
• So, there are 4 different bottle sizes possible. The correct answer is (b).