Published by:
CGP EDU Academic Team
Published on: August 11, 2026
If 500 ! = 2m x an integer, then
A
m = 494
B
m = 496
C
Is equivalent to number of m is 400 ! = 2 n xan integer
D
m = 
Text Solution
Verified by ExpertsThe correct answer is:
A
Here we have to count “2” in 500!, To get this count only one “2” from
(i) Multiple of 2 i.e., 2, 4, 6,... 500 ≡ ≡ 250
(ii) Multiple of 4 i.e., 4, 8, 12, ...500 ≡ ≡ 125
(iii) Multiple of 8 i.e., 8, 16, 24, ... 496 ≡ ≡ 62
(iv) Multiple of 16 i.e., 16, 32, 48, .... 496 ≡ ≡ 31
(v) Multiple of 32 i.e., 32, 64, 96, ... 480 ≡ ≡ 15
(vi) Multiple of 64 i.e., 64, 128, ... 448 ≡ ≡ 7
(vii) Multiple of 128 i.e., 128, 256, 384 ≡ ≡ 3
(viii) Multiple of 256 i.e., 256 ≡ ≡ 1
∴ ∴ Total = 494
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