Question

Product of first ten natural numbers=2a=(3b)(5c)(7d) then find the value of a+b+c+d​

Answer 1

The question needs correction

It will be replaced by $\sf{2^a\times3^b\times5^c\times7^d}$

Solving the Question

We all know that the first ten natural numbers are

• 1, 2, 3, 4, 5, 6, 7, 8, 9

But in prime factorization form

• 1, 2, 3, 2², 5, 2×3, 7, 2³, 3²

After summing exponent of 2, 3, 5, 7

• $\sf{a=1+2+1+3=7}$
• $\sf{b=1+1+2=4}$
• $\sf{c=1}$
• $\sf{d=1}$

For your information.

1. If the exponent is not shown, the number must have an exponent of 1.

Because we don't show it formally.

2. We sum each exponent when we multiply.

Answer 2

Answer:

Ans = 14

Step-by-step explanation:

First ten natural numbers are 1,2,3,4,5,6,7,8,9,10

We can write the product as 1*2*3*(2*2)*5*(2*3)*7*(2*2*2)*(3*3)*(2*5)

That is:

2^7 * 3^4* 5^2* 7

That is:

a=7

b=4

c=2

d=1

a+b+c+d= 7+4+2+1=14