Question

. If the product of first ten natural numbers is expressed in the form of 2^a × 3^b× 5^c× 7^d, then find the value of a + b + c + d.

Answer 1

ANSWER

PRODUCT OF FIRST 10 NATURAL NUMBERS

1×2×3.........up to 10

since factor of

1 = 1

2 = 2 ×1

3 = 3×1

4 = 2×2×1

5 = 5×1

6 = 2×3×1

7 = 7×1

8 =2×2×2×1

9 = 3×3×1

10 = 2×5×1

and we know a × a = a ^(1+1) = a^2

so product of first ten natural numbers can be written as

2^8 3^4 5^2 7^1

on comparing

a = 8

b=4

c = 2

d = 1

if question tell that product of first 200

then in such situation

first calculate factorial of 200 then

then use prime factorisation then make pairs of 2 3 4 5 6 7 8 9

and get your result

hope it helps

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