Question 1 - Figure it out - Page 59 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

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Question 1 (a) Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. (a) Two consecutive even numbers Two consecutive even numbers could be 2 & 4, or 10 & 12 We note that The only number that divides two neighbor even numbers is 2 Thus, HCF is always 2. Question 1 (b) Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. (b) Two consecutive odd numbers Two consecutive odd numbers could be 3 & 5, or 9 & 11 We note that They don't share any factors except 1. Thus, HCF is always 1 Question 1 (c) Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. (c) Two even numbers Two even numbers could be 4 & 8, or 6 & 10 We note that Both can always be divided by 2 . Thus, HCF is always at least 2 (it could be larger) And, HCF is always even number Question 1 (d) Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. (d) Two consecutive numbers Two consecutive numbers could be 4 & 5, or 15 & 16 We note that Two consecutive numbers never share any factors except 1 Since there is only 1 as common factor., ∴ HCF is always 1 Question 1 (e) Make a general statement about the HCF for the following pairs of numbers. You could consider examples before coming up with general statements. Look for possible explanations of why they hold. (e) Two co-prime numbers Two co-prime numbers could 4 & 9 Now Co-prime numbers mean they have no common factor other than 1 Since there are no common factors other than 1, it means their HCF is always 1