Question 2 - Page 48 - The Greatest of All - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

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Question 2 - Page 48 Do you remember the ‘Jump Jackpot’ game from Grade 6 (see the chapter ‘Prime Time’)? Grumpy places a treasure on a number and Jumpy chooses a jump size and tries to collect the treasure. In each case below, the two numbers upon which treasures are kept are given. Find the longest jump size (starting from 0) using which Jumpy can land on both the numbers having the treasure. (a) 14 and 30 (b) 7 and 11 (c) 30 and 50 (d) 28 and 42In the "Jump Jackpot" game, a player named Grumpy places two treasures on two different numbers. Jumpy must choose a single jump size that allows him to land on both treasure numbers, starting his jumps from 0. For (a) - Treasures are placed on 14 and 30 If Jumpy chooses a jump size of 7, he will jump to 7→14→21→28→35→42.... In this case, he lands on 14 but does not land on 30, so he does not win the treasures. To find a winning jump size, Jumpy must choose a number that is a factor of both treasure locations. And since he wants longest jump size, he wants to find the Highest Common Factor (HCF) Finding HCF of 14 & 30 Factors of 14 are: 1, 2, 7, 14 Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30 The Common Factors are: 1, 2 Thus, the Highest Common Factor (HCF) is 2. So, Jumpy should do a longest jump of 2 For (b) - Treasures are placed on 7 and 11 Here, Longest jump size = Highest Common Factor (HCF) Finding HCF of 7 & 11 Factors of 7 are: 1, 7 Factors of 11 are: 1, 11 The Common Factors are: 1 Thus, the Highest Common Factor (HCF) is 1. So, Jumpy should do a longest jump of 1 For (c) - Treasures are placed on 30 and 50 Here, Longest jump size = Highest Common Factor (HCF) Finding HCF of 30 & 50 Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30 Factors of 50 are: 1, 2, 5, 10, 25, and 50 The Common Factors are: 1, 2, 5, 10 Thus, the Highest Common Factor (HCF) is 10 So, Jumpy should do a longest jump of 10 For (d) - Treasures are placed on 28 and 42 Here, Longest jump size = Highest Common Factor (HCF) Finding HCF of 28 & 42 Factors of 28 are: 1, 2, 4, 7, 14, and 28 Factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42 The Common Factors are: 1, 2, 7, 14 Thus, the Highest Common Factor (HCF) is 14 So, Jumpy should do a longest jump of 14