What is the greatest number that divides 1803 and 2028 a remainder of 3 in each case ? ​

Question

What is the greatest number that divides 1803 and 2028
a remainder of 3 in each case ? ​

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Eden 2 weeks 2021-09-04T02:04:47+00:00 2 Answers 0 views 0

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    0
    2021-09-04T02:05:48+00:00

    _____Answer _________

    Here, we need to find differences between the given numbers. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number.

    Our numbers here are 91−43=48,183−91=92,183−43=140

    So we have the set of numbers {48,92,140} and we want to know the biggest number that divides all these numbers.

    So,

    48=2×2×2×3

    92=2×2×23

    140=2×2×5×7

    The greatest common divisor of {48,92,140} is 4.

    So, answer is 4.

    0
    2021-09-04T02:06:34+00:00

    Step-by-step explanation:

    1803-3=1800

    2028-3=2025

    1800=2×2×2×3×3×5×5

    2025=3×5×5×5×5

    HCF=3×5×5

    =75

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