Question

Find the largest number that divides 189, 223, 347 leaving remainders 9, 3, 7 respectively in each case

Answer 1

Step 1 : Subtract 9, 3 & 7 from 189, 223 & 347

189 - 9 = 180

223 - 3 = 220

347 - 7 = 340

Step 2 : Find the prime factors of the obtained numbers

180 = 2 × 2 × 3 × 3 × 5

220 = 2 × 2 × 5 × 11

340 = 2 × 2 × 5 × 17

Step 3 : Find the HCF of the numbers

First let's find the common factors of the new numbers.

Common factors = 2 × 2 × 5 = 20

The product of the common factors is the HCF of the numbers.

∴ HCF = 20

∴ The largest number that divides 189, 223, 347 leaving remainders 9, 3, 7 respectively in each case is 20

Answer 2

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Subtract  the following First :-

189 - 9 = 180

223 - 3 = 220

347 - 7 = 340

LCM of 180 , 220 , 340

180 = 2 × 2 × 3 × 3 × 5

220 = 2 × 2 × 5 × 11

340 = 2 × 2 × 5 × 17

Common factor = 2 × 2 × 5 = 20

HCF = 20

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