1. Дасгалын зорилго нь энгийн бутархайг хамгийн ихээр хурааж, хамгийн энгийн хэлбэрт оруулах юм. 2. Бутархайг хураахад хамгийн гол зүйл бол тооны хамгийн их нийт хуваагч (ХИЕК)-ийг олох. 3. ХИЕК ашиглан тухайн бутархайн тоонуудыг хуваана. Жишээ: - 15 / 75 = $\frac{15 \div 15}{75 \div 15} = \frac{1}{5}$ - 75 / 100 = $\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$ (шалгаж буй дүрс ангилагчыг харж хамааруулаарай) - 54 / 88 = $\frac{54 \div 2}{88 \div 2} = \frac{27}{44}$ - 32 / 100 = $\frac{32 \div 4}{100 \div 4} = \frac{8}{25}$ - 82 / 24: ХИЕК(82, 24) = 2, $\frac{82 \div 2}{24 \div 2} = \frac{41}{12}$ - 88 / 121: ХИЕК(88, 121) = 11, $\frac{88 \div 11}{121 \div 11} = \frac{8}{11}$ - 32 / 18: ХИЕК(32, 18) = 2, $\frac{32 \div 2}{18 \div 2} = \frac{16}{9}$ - 45 / 36: ХИЕК(45, 36) = 9, $\frac{45 \div 9}{36 \div 9} = \frac{5}{4}$ - 32 / 24: ХИЕК(32, 24) = 8, $\frac{32 \div 8}{24 \div 8} = \frac{4}{3}$ - 175 / 200: ХИЕК(175, 200) = 25, $\frac{175 \div 25}{200 \div 25} = \frac{7}{8}$ - 1400 / 1000: ХИЕК(1400, 1000) = 100, $\frac{1400 \div 100}{1000 \div 100} = \frac{14}{10} = \frac{7}{5}$ - 300 / 500: ХИЕК(300, 500) = 100, $\frac{300 \div 100}{500 \div 100} = \frac{3}{5}$ - 250 / 300: ХИЕК(250, 300) = 50, $\frac{250 \div 50}{300 \div 50} = \frac{5}{6}$ - 400 / 120: ХИЕК(400, 120) = 40, $\frac{400 \div 40}{120 \div 40} = \frac{10}{3}$ - 50 / 60: ХИЕК(50, 60) = 10, $\frac{50 \div 10}{60 \div 10} = \frac{5}{6}$ - 70 / 80: ХИЕК(70, 80) = 10, $\frac{70 \div 10}{80 \div 10} = \frac{7}{8}$ - 69 / 92: ХИЕК(69, 92) = 23, $\frac{69 \div 23}{92 \div 23} = \frac{3}{4}$ - 125 / 1000: ХИЕК(125, 1000) = 125, $\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$ - 6 / 51: ХИЕК(6, 51) = 3, $\frac{6 \div 3}{51 \div 3} = \frac{2}{17}$ - 8 / 68: ХИЕК(8, 68) = 4, $\frac{8 \div 4}{68 \div 4} = \frac{2}{17}$ - 15 / 85: ХИЕК(15, 85) = 5, $\frac{15 \div 5}{85 \div 5} = \frac{3}{17}$ - 17 / 51: ХИЕК(17, 51) = 17, $\frac{17 \div 17}{51 \div 17} = \frac{1}{3}$ - 34 / 102: ХИЕК(34, 102) = 34, $\frac{34 \div 34}{102 \div 34} = \frac{1}{3}$ - 68 / 170: ХИЕК(68, 170) = 34, $\frac{68 \div 34}{170 \div 34} = \frac{2}{5}$ - 38 / 57: ХИЕК(38, 57) = 19, $\frac{38 \div 19}{57 \div 19} = \frac{2}{3}$ - 57 / 60: ХИЕК(57, 60) = 3, $\frac{57 \div 3}{60 \div 3} = \frac{19}{20}$ - 76 / 36: ХИЕК(76, 36) = 4, $\frac{76 \div 4}{36 \div 4} = \frac{19}{9}$ - 95 / 100: ХИЕК(95, 100) = 5, $\frac{95 \div 5}{100 \div 5} = \frac{19}{20}$ - 152 / 190: ХИЕК(152, 190) = 38, $\frac{152 \div 38}{190 \div 38} = \frac{4}{5}$ - 171 / 81: ХИЕК(171, 81) = 9, $\frac{171 \div 9}{81 \div 9} = \frac{19}{9}$ - 49 / 147: ХИЕК(49, 147) = 49, $\frac{49 \div 49}{147 \div 49} = \frac{1}{3}$ - 42 / 91: ХИЕК(42, 91) = 7, $\frac{42 \div 7}{91 \div 7} = \frac{6}{13}$ - 51 / 91: ХИЕК(51, 91) = 17, $\frac{51 \div 17}{91 \div 17} = \frac{3}{7}$ - 72 / 810: ХИЕК(72, 810) = 18, $\frac{72 \div 18}{810 \div 18} = \frac{4}{45}$ - 680 / 340: ХИЕК(680, 340) = 340, $\frac{680 \div 340}{340 \div 340} = \frac{2}{1}$ - 270 / 300: ХИЕК(270, 300) = 30, $\frac{270 \div 30}{300 \div 30} = \frac{9}{10}$ - 28 / 49: ХИЕК(28, 49) = 7, $\frac{28 \div 7}{49 \div 7} = \frac{4}{7}$ - 45 / 81: ХИЕК(45, 81) = 9, $\frac{45 \div 9}{81 \div 9} = \frac{5}{9}$ - 6 / 9: ХИЕК(6, 9) = 3, $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$ - 9 / 18: ХИЕК(9, 18) = 9, $\frac{9 \div 9}{18 \div 9} = \frac{1}{2}$ - 72 / 380: ХИЕК(72, 380) = 4, $\frac{72 \div 4}{380 \div 4} = \frac{18}{95}$ - 4 / 12: ХИЕК(4, 12) = 4, $\frac{4 \div 4}{12 \div 4} = \frac{1}{3}$ - 13 / 64: ХИЕК(13, 64) = 1, энгийн хэлбэр (үгүйг орхих) - 72 / 90: ХИЕК(72, 90) = 18, $\frac{72 \div 18}{90 \div 18} = \frac{4}{5}$ - 65 / 130: ХИЕК(65, 130) = 65, $\frac{65 \div 65}{130 \div 65} = \frac{1}{2}$ - 93 / 27: ХИЕК(93, 27) = 3, $\frac{93 \div 3}{27 \div 3} = \frac{31}{9}$ - 128 / 512: ХИЕК(128, 512) = 128, $\frac{128 \div 128}{512 \div 128} = \frac{1}{4}$ - 56 / 64: ХИЕК(56, 64) = 8, $\frac{56 \div 8}{64 \div 8} = \frac{7}{8}$ Эцэст нь: ХИЕК ашиглан бутархай бүрийг хамгийн энгийн хэлбэрт хурааж чадна.