Question (e) - Page 51 (Figure it out) - Prime Factorisation - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

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Question (e) - Page 51 (Figure it out) List all the factors of the following numbers: (e) 840 (this number has 32 factors)Let’s do Prime Factorisation of 840 So, we can write 840 = 2 × 2 × 2 × 3 × 5 × 7 Now, Factors would be Prime Factors Combination of prime factors And, number 1 Let’s look at each one of them Prime Factors: Prime Factors are 2, 3, 5, 7 Combination of two prime factors: Factors are 2 × 2 = 4 2 × 3 = 6 2 × 5 = 10 2 × 7 = 14 3 × 5 = 15 3 × 7 = 21 5 × 7 = 35 Combination of three prime factors: Factors are 2 × 2 × 2 = 8 2 × 2 × 3 = 12 2 × 2 × 5 = 20 2 × 2 × 7 = 28 2 × 3 × 5 = 30 2 × 3 × 7 = 42 2 × 5 × 7 = 70 3 × 5 × 7 = 105 Combination of four prime factors: Factors are 2 × 2 × 2 × 3 = 24 2 × 2 × 2 × 5 = 40 2 × 2 × 2 × 7 = 56 2 × 2 × 3 × 5 = 60 2 × 2 × 3 × 7 = 84 2 × 2 × 5 × 7 = 140 2 × 3 × 5 × 7 = 210 Combination of five prime factors: Factors are 2 × 2 × 2 × 3 × 5 = 120 2 × 2 × 2 × 3 × 7 = 168 2 × 2 × 2 × 5 × 7 = 280 2 × 2 × 3 × 5 × 7 = 420 Combination of six prime factors: Factors are 2 × 2 × 2 × 3 × 5 × 7 = 840 Thus, Factors of 840 (32 factors) are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840