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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , 22., , 23., , Number of odd factors of 2000 is?, , 30 = 21×31×51, , 2000 ds, , = (30+31)(50+51), , (a) 4, , (b) 3, , = 4×6 = 24, , (c) 5, , (d) 7, , Sum of odd factor = 24, , xq.ku[k.Mksa dk ;ksx D;k gS\, , 40 = 23×5, , (b) 403, , = (50+51) = 6, , (c) 400, , (d) 15, , Sum of odd factor = 6, , 4., , What is the sum of factors of 140?, , (b), 100 = 22×52, , xq.ku[k.Mksa dk ;ksx D;k gS\, , (a) 336, , (b) 672, , = (50+51+52) = 31, , (c) 4, , (d) 12, , Sum of odd factor = 31, , 5., , What is the total number of factors of 165?, , (c), , 165 ds dqy xq.ku[k.Mksa dh la[;k D;k gS\, , 760 = 23×51×191, , (a) 3, , (b) 8, , = (50+51)(190+191) = 6×20 = 120, , (c) 4, , (d) 6, 6., , 1, 6, 11, 16, 21, , (d), , (a) 806, , 140 ds, , 25., , 3., , What is the sum of factors of 144?, 144 ds, , 24., , fo"ke xq.ku[k.Mksa dh la[;k gS\, , d, c, d, d, b, , 2, 7, 12, 17, 22, , a, d, a, a, a, , Answer Key, 3, d, 8, b, 13 c, 18 a, 23 b, , (c), 240 = 24×31×51, , 4, 9, 14, 19, 24, , b, c, b, c, a, , 5, 10, 15, 20, 25, , c, b, b, a, b, , 240 = 24×31×51, All factor = (4+1)(3+1)(1+1), = 5×2×2 = 20, even factor = 4×2×2 = 16, odd factor = 2×2 = 4, , Solutions, 1., , (d), , 7., , 20 = 22×51 = (50+51) = 6, , (d), 980 = 22×51×72, , Sum of odd factor = 6, , All factor = (20+21+22)(50+51)(70+71+72), , Note : bl case esa dsoy fo"ke vHkkT; la[;kvksa dks gh ysxs, , = 7×6×57 = 2394, even, , 2., , (a), 3, , = (21+22)(50+51)(70+71+72)

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , = 6×6×57 = 2052, odd, , No. of prime factor = 4, , = (50+51)(70+71+72), = 6×57 = 342, , 12., , (a), = 27×344×2536×133, , 8., , (b), , 2, 2, 3, 180 , 3, 5, , = 27×344×527×133, Prime factor = 2, 3, 5, 13, , 80, 90, 45, 15, 5, 1, , No. of prime factor = 4, , 13., , (c), Any factor of this number should be of form of, 2a×3b×5c for factor to be an odd no., , 180 = 2×2×3×3×5, , a should be always 0., , 180 = 22×32×51, , b can take values 0,1,2,3,4,5; total 6 values, , No of prime factor = 2+2+1 = 5, , c can take values 0,1,2,3,4,5,6,7; total 8 values, 9., , Total numbers of odd factors = 6×8 = 48, , (c), , OR, , 100  22×52, (b+1) (c+1) = 48, , Prime Factor = 2, 5, No. of Prime factor = 2, 14., 10., , (b), Prime factors of 24×56×78×107, , (b), , 211×513×78 = 2a×5b×7c, , =65×103×34×492, , Even factors = (a) (b+1) (c+1) = 11×14×9 =, 1386, , =25×35×23×53×34×74, = 28×39×53×74, Prime factor = 2, 3, 5, 7, , 15., , No. of prime factor = 4, , (b), Prime factors of 3500 = 22×53×7, No. of even factors = (a)(b+1) (c+1), , 11., , (d), =, , So 2×4×2 = 16, , 364×1012×274×113×1236, , = (22×32)4×(2×5)12×(33)4×113×(22×3)36, =, , 28×38×212×512×312×113×272×336, , =, , 292×356×512×113, , 16., , (d), 20 = 1 = so there is no any even factor., , Prime factor = 2, 3, 5, 11, , 17., , 4, , (a)

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Edited with the trial version of, Foxit Advanced PDF Editor, To remove this notice, visit:, www.foxitsoftware.com/shopping, , Prime factors of 117×52×34×7×104, , No. of odd factors = (b+1) = 4, , = 23×34×56×7×117 = 2a×3b×5c×7d×11e, So No. of factors = (b+1)(c+1)(d+1)(e+1), , 18., , 23., , (b), , = 5 × 7 × 2 × 8 = 560, , Prime factors of 144 = 24×32, , (a), , Now this No. should be of form 2a×3b, , Prime factorization of 56 = 23×7, ,  a 1  1   3b1 , , ,  21   31 , ,  , , , 2, Here sum of factors  , , This should be in the form = 2a×7b, ,  25  1  33  1 , ,   31  13  403, ⇒, ,  2a 1  1   7b1  1 , , ,  21   7 1 , , , , , So formula ⇒ (1) , , (2) (20+21+……..2a+1), , (71+72+…7a+1), ,  24  1  72  1 , , , So , , ⇒, ,  2  1  7  1 , , , , , , , , 2, , 1, , 2, , 3, , 2 2 2, , 7, , 0, , 1, , 7, , , , , 2, , , , , OR, , 20  21  22  23  24 30  31  32  ⇒ 31×13 = 403, , 15 48, ,  120, 1 6, , OR, 0, , 1, , 24., ,  ⇒ 15×8 = 120, , (a), Prime factorization of 140 = 22×5×7, This should be of form, , 19., , 20., , = 2a×5b×7c, , (c), , Sum of factors is, , No. 8 total factors = 24×31×53 = 5×2×4 = 40, ,  2a 1  1  5b1  1  7c 1  1 , , , , ,  2  1  5  1  7  1 , , , , , , (a), ,  23  1  52  1  72  1 , 7 24 48, , ,  =  , ⇒, = 7×6×8,  2  1 , , , , Prime factorization of 64 = 26, , 4, , , , , 6, , , , , 1, , 4, , 6, , = 336, , Here the prime factor is only 2, So. Number of prime factors is 1, , 25., , (b), Prime factorization of 165 = 3×5×11, , 21., , (b), , This should be of form = 3a×5b×11c, , Prime factorization of 1500 = 22×3×53 for odd, factors this number should be of form =, 2a×3b×5c, , Now total factors = (a+1) (b+1)(c+1) =, (1+1)(1+1)(1+1) = 2×2×2 = 8, , Now No. of odd factors = (b+1)(c+1) ⇒, (1+1)(3+1) = 2×4 = 8, , 22., , (a), Prime factorization of 2000 = 24×53, So it should be in the form of = 2a×5b, , 5