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Bases Math Question?
In what bases, b, does (b + 10) divide into (8b + 10) without any remainder?
1 Answer
- SamwiseLv 71 year agoFavorite Answer
Let q represent the quotient. Then
8b + 10 = q (b + 10) = qb + 10q
and plainly 1 < q < 8 .
(8-q) b = 10q - 10 = 10 (q - 1)
b = 10 (q - 1) / (8 - q)
Considering the possible values for q, we find that
if q=7, b=60
if q=6, b=25
if q=5, b=40/3
if q=4, b=15/2
if q=3, b=4
if q=2, b=10/3
Obviously, we need b to be an integer, so let's see if these three really work:
b=60: 8b+10 = 490 and b+10 = 70 divides it.
b=25: 8b+10 = 210 and b+10 = 35 divides it.
b=4: 8b+10 = 42 and b+10 = 14 divides it.
