find the gretest number which divides 230 , 1314 and 1331 and living the remainder 5 in each case
Answers
Step-by-step explanation:
The question is the largest number that we can divide 230; 1314; and 1331 by and have a remainder of 5 in each case.
230 – 5 = 225
Factor 225 into prime numbers; 5 * 45 = 5 * 5 * 3 * 3
1314 – 5 = 1309
Factor 1309 into prime numbers; 7 * 187 = 7 * 11 * 17
1331 – 5 = 1326
Factor 1326 into prime numbers; 2 * 663 = 2 * 3 * 221 = 2 * 3 * 13 * 17
No common integer factors to all three numbers, therefore the solution is not an integer.
So we need to seek a real number solution to:
aX = (230 – 5); bX = (1314 – 5); cX = (1331 – 5) for integer values of a; b; and c
aX + 5 = 230; aX = 225, X = 225/a = 1314/b = 1326/c; 1/X = a/225 = b/1309 = c/1326
bX + 5 = 1314; bX = 1309
cX + 5 = 1331; cX = 1326
solve for X;
a; b; and c must be integers
a = 225b/1309 = 225c/1326; a = (2 * 2 * 3 * 3)b/(7 * 11 * 17) = (2 * 2 * 3 * 3)c/(2 * 3 * 13 * 17)
if b = 77; c = 78, then X = 225 * 77/1309 = 13.23529411764706; X = 225 * 78/1326 = 13.23529411764706
a = 17; b = 77; c = 78; X = 13.23529411764706 (approximately, this a real but not rational number); so divide the three numbers by 225 * 78/1326 or 2925/221or approximately 13.23529411764706
Answer:
So, 17 is the HCF and it is the greatest number which divides 260, 1314 and 1331 and leaves remainder 5 in each case.
Step-by-step explanation:
please make me brainlist