Question

product of first ten natural numbers =2n×3b ×5c×7d then find the value of a+b+c+d​

Answer 1

Hope it helps u.........

Answer 2

Given:

product of the first ten natural numbers =$2^{a}.3^{b}.5^{c}.7^{d}$

To find:

The value of a+b+c+d

Solution:

As we know that the natural numbers are:

1,2,3,4,5......................... and so on till infinity

we have the first 10 natural number as:

• 1×2×3×4×5×6×7×8×9×10

now we will break the terms in the multiplication of the prime numbers

• 1×2×3×2×2×5×2×3×7×2×2×2×3×3×2×5

we get the exponent as:

$2^{8}.3^{4}.5^{2}.7^{1}$

on comparing we get the value of a,b,c and, d as:

• a = 8
• b = 4
• c = 2
• d = 1

So,

the value of the term a+b+c+d = 8+4+2+1 = 15

The value of a+b+c+d is 15