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What number can be a number that divides 171 with a remainder of 6 list all the two digit numbers that number can be?
If the result has a remainder of 6, then the number must be 165 + 6.
So you need to find all the 2-digit factors of 165.
The easiest way is to just start listing them and see what you get.
Start with 10, then go to 11, etc and write the factor pairs.
If some number is not a factor of 165, just skip it and go to the next number.
When the factors start to repeat, you are done.
The two-digit factors of 165
10 × ___ <-- 10 is not a factor, so skip it and go to the next number
11 × 15
12 × ___ <-- Not a factor. Skip to the next number
13 × ___ <-- Not a factor
14 × ___ <-- Skip this one
15 × 11 <-- The factors are repeating, so you are done.
Answer:
The only two-digit numbers that divide 171 with a remainder of 6 are
11 and 15
Check
171 ÷ 11 = 15 R6
171 ÷ 15 = 11 R6
Check!
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