Question

If 500 ! = 2m x an integer, then

• A. m = 494
• B. m = 496
• C. Is equivalent to number of m is 400 ! = 2ⁿxan integer
• D. m = $500C_{2}$

Answer 1

Answer: (A)

m = 494

Answer 2

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