# What number is divisible by 294?

## Step by step math 2, workbook

1 Divisibility 23 a) | b) | c) | d) | e) | f) | g) | h) | i) | 24 a) 10, 15 b) 30 c) 12, 16 d) 5, 7 e) 2, 3, 6, 11, 22, 33 f) 30, 36 25 Compare with the drawings of part a! a) rectangle: 3 x 4; T 12 = {1, 2, 3, 4, 6, 12} b) rectangles: 1 x 20, 2 x 10 or 4 x 5; T 20 = {1, 2, 4, 5, 10, 20} c) rectangle: 1 x 4, square: 2 x 2; T 4 = {1, 2, 4} d) rectangle: 1 x 9, square: 3 x 3; T 9 = {1, 3, 9} 26 Yes, 25 | 250, each child receives 10 €. 27 Number of children: 12 or 24 (higher numbers of schoolchildren are not allowed in Austria.) Rows of six are possible. If there are 24 or more pupils, they could line up in groups of eight, twelve or twenty-four. 28 a) V 12 = {12, 24, 36, 48, 60, 72, ...} b) V 13 = {13, 26, 39, 52, 65, 78, ...} c) V 9 = {9, 18 , 27, 36, 45, 54, ...} d) V 92 = {92, 184, 276, 368, 460, ...} 29 T 2 = {1, 2}; T 4 = {1, 2, 4}; T 5 = {1.5}; T 10 = {1, 2, 5, 10} 30 a) Yes, 2 | 20 b) Yes, 4 | 20 c) sensible: single chairlift: 1 | 20, five-person chairlift: 5 | 20; does not make sense: ten-seat chair lift: 10 | 20, Zwanziger chairlift: 20 | 20 d) Large gondola for 20 people, small gondola for 10 people or five-person chairlift 31 a) 46, 48, 50, 52, 54, 56, 58 b) 48, 52, 56 c) 45, 50, 55 32 3 400, 3 404, 3 408, 3 412, 3 416, 3 420, 3 424, 3 428, 3 432, 3 436, 3 440, 3 444, 3 448, 3 452, 3 456, 3 460, 3 464, 3,468, 3,472, 3,476, 3,480, 3,484, 3,488, 3,492, 3,496 33 e.g. E.g .: 6 | 25; 33 | 66; 2 | 192; 5 | 19; 50 | 100; 5 | 515 34 e.g. E.g .: a) 2,307,584, 2,378,540, 4,307,852; ... b) 2 307845, 2 347850, 2 378 450; ... 35 blue: 93, 993, 732, 309, 96; red: 9756, 9 396, 27, 369 072, 351, 774 36 a) | b) | c) | d) | e) | 37 Yes, 3 | 123; 41 pieces per shelf 38 a) 204, 234, 264, 294 b) 672, 675, 678 c) 309, 339, 369, 399 d) 327, 627, 927 e) 501, 504, 507 39 Solution: DENKSPORT 40 a ) 99 999; 10 002 b) 99 999; 10 008 41 circles one: 5, 11, 41 42 a) 14 = 2 7 b) 27 = 3 3 3 c) 60 = 2 2 3 5 d) 140 = 2 2 5 7 43 SHARE 44 e.g. For example: 5751 is not a prime number because numbers whose sum of digits is divisible by 3 or 9 are divisible by 3 or 9. 2 302 is not a prime number because numbers with a final digit of 2 are divisible by 2. 975 is not a prime number because numbers with a final digit of 5 are divisible by 5, and the sum of digits is also divisible by 3. 45 a) 180 = 2 2 3 3 5 b) 378 = 2 3 3 3 7 c) 945 = 3 3 3 5 7 d) 1 890 = 2 3 3 3 5 7 46 A: true, B: false, C: true, D: false 47 a) gcd (30, 45) = 15 b) gcd (16, 24) = 8 c) gcd (24, 56 ) = 8 48 gcd (6, 8, 12) = 2; 2m 49 z. E.g .: a) gcd (10, 15) = 5; gcd (15, 35) = 5; ... b) gcd (14, 35) = 7; gcd (35, 49) = 7; ... 50 a) gcd (15, 20) = 5; Tile: 5m x 5m b) A = 300m 2; 12 Tiles K K 3 For testing purposes only a a - Property of the publisher öbv