What is the largest integer divisible by 15
Answers
Answer:
➡ 33.........
hoping this is helpful to u☺
Answer:
the answer wiilll be 33
Step-by-step explanation:
ANSWER
Sol :- Given,
To prove that 33! is divisible by 2
15
as we know that,
33!=33×32×31×30×−−−×8×7×6×5×4×3×2×1
33!=33×(2)
5
×31×30×−−−−(2)
3
×7×6×5×(2)
2
×3(2)
1
×1
let us now consider all the 2's form the
above configuration, we get
33!=2
5
×2
4
×2
3
×2
2
×2
1
(33×31×30×−−−×6×5×3×1)
33!=2
5+4+3+2+1
(33×31×30×−−−×6×5×3×1)
33!=2
15
(33×31×30×−−−×6×5×3×1) → eq(1)
33!=2
15
(33!)
2
15
=
33!
33!
=1
∴ 33! is divisible by 2
15
Hence Proved → proved.
Now, let us find the value of 2
n
having considered all the 2 terms
in the configuration we get the
value of 2
n
=2
16
Let us substitute this in eq(1) we get,
33!=2
15
.2
16
33!=2
31
we can now say that 31 is the largest
number such that 33! is divisible by 2
n
Hence Proved