Answered

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what is the greatest number that can divide 13,17 and 21 and have one as a remainder​

Sagot :

Reinhard10158idn

Answer:

4

Step-by-step explanation:

this is the same question as what number can divide

13-1 = 12, 17-1 = 16 and 21-1 = 20 and has 0 remainder ?

the greatest number that can do that is 4.

we can easily see that, but formally, let's do prime factorization :

12 ÷ 2 = 6

6 ÷ 2 = 3

3 ÷ 2 no

3 ÷ 3 = 1 finished

12 = 2×2×3

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 finished

16 = 2×2×2×2

20 ÷ 2 = 10

10 ÷ 2 = 5

5 ÷ 2 no

5 ÷ 3 no

5 ÷ 5 = 1 finished

20 = 2×2×5

so, the largest common factor is the combination of the longest streaks per factor they have in common.

they only have 2s in common.

and the longest common streak is 2×2 = 4.

hence the answer

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