find the greatest number which divides 1750 and 2000 leave 48 and 2 respectively as remainder
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1750 - 48 = 1702, so the number which we need divides 1702 completely.
2000 - 2 = 1998, so the number which we need divides 1998 completely.
Thus, we need to find the greatest common factor of 1702 and 1998.
If you were to use a calculator, you will realise that number is 74, since 1702/1998 = 23/27, and 1702 = 23 * 74.
If you are not allowed to use this method, you will need to use euclidean algorithm:
1998 = 1702(1) + 296
1702 = 296(5) + 222
296 = 222(1) + 74
222 = 74(3) + 0
Since the last non-zero remainder is 74, the GCD of both numbers is 74, which in turn mean the number which we need is 74.
2000 - 2 = 1998, so the number which we need divides 1998 completely.
Thus, we need to find the greatest common factor of 1702 and 1998.
If you were to use a calculator, you will realise that number is 74, since 1702/1998 = 23/27, and 1702 = 23 * 74.
If you are not allowed to use this method, you will need to use euclidean algorithm:
1998 = 1702(1) + 296
1702 = 296(5) + 222
296 = 222(1) + 74
222 = 74(3) + 0
Since the last non-zero remainder is 74, the GCD of both numbers is 74, which in turn mean the number which we need is 74.
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