Question

A wholesale tea dealer has 408kg, 468kg and 516kg of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box

thank you^-^

Answer 1

We will take HCF of these numbers

408 = 2x2x2x3x17

468 = 2x2x3x3x13

516 = 2x2x3x43

So HCF is 2x2x3 coz these three numbers are common in 408, 468, 516

hence 12 is the HCF

Answer 2

Find the Prime Factors :

408 = 2³ x 3 x 17

468 = 2² x 3² x 13

516 = 2² x 3 x 43

Find the HCF:

HCF = 2² x 3 = 12

⇒ 12 is the highest common factors of the 4 numbers

Therefore capacity of the largest box is 12 kg

Additional Information :

408 kg = 408 ÷ 12 = 34 boxes of 12 kg

468 kg = 468 ÷ 12 = 39 boxes of 12 kg

516 kg = 516 ÷ 12 = 43 boxes of 12 kg