Question 1 - Page 48 - The Greatest of All - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 1 - Page 48 Lekhana purchases rice from two farms and sells it in the market. She bought 84 kg of rice from one farm and 108 kg from the other farm. She wants the rice to be packed in bags, so each bag has rice from only one farm and all bags have the same weight that is a whole number of kg. If she wants to use as few bags as possible, what should the weight of each bag be? Given Two bags of rice weight 84 kg & 108 kg. . She wants to pack them into bags that are all the same weight. he wants the bags to be as heavy as possible (so she uses fewer bags). Thus, we need to find A number that divides both 84 and 108 exactly And, it should be largest possible Thus, we need to find Highest Common Factor of 84 & 108 Now, Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. The Common Factors are: 1, 2, 3, 4, 6, and 12 Thus, the Highest Common Factor (HCF) is 12. So, She should make each bag weigh 12 kg. Note: Finding factors of individual numbers is very tedious and time consuming. Practically, we find HCF using Prime Factorisation