Question 69

Find the greatest number that will divide 115, 149 and 183 leaving remainders 3, 5, 7 respectively.

Solution

115, 149 and 183 leaving remainders 3, 5, 7

HCF of (115 - 3, 149 - 5, 183 - 7)

⇒ HCF of (112, 144, 176)

112 = $$2\times 2\times 2\times 2\times 7 $$

144= $$2\times 2\times 2\times 2\times 3\times 3$$

176 = $$2\times 2\times 2\times 2\times 11$$

16 is hcf that will divide 115, 149 and 183 leaving reminder 3, 5, 7 respectively

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