Find the largest number that divides 189, 223, 347 leaving remainders 9, 3, 7 respectively in each case
Answers
Answered by
126
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
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Answered by
66
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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