the largest odd factor of 6^8 * 10^6 is
A (6^8 * 10^6)/2
B 3^4 * 5^3
C 15^6
D 3^8 * 5^6
6⁸ ∙ 10⁶ = ( 2 ∙ 3 )⁸ ∙ ( 2 ∙ 5 )⁶ = 2⁸ ∙ 3⁸ ∙ 2⁶ ∙ 5⁶ = 2⁸ ∙ 2⁶ ∙ 3⁸ ∙ 5⁶ = 2¹⁴ ∙ 3⁸ ∙ 5⁶
2¹⁴ is event
3⁸ is odd
5⁶ is odd
D.
3⁸ ∙ 5⁶
Thanks
To find the largest odd factor of a number, we need to prime factorize the number and then select all the factors that contain only odd prime numbers.
Let's factorize 6^8 * 10^6:
6^8 = (2 * 3)^8 = 2^8 * 3^8
10^6 = (2 * 5)^6 = 2^6 * 5^6
Combining the two:
6^8 * 10^6 = 2^8 * 3^8 * 2^6 * 5^6 = 2^(8+6) * 3^8 * 5^6 = 2^14 * 3^8 * 5^6
To get the largest odd factor, we need to only consider the odd prime numbers, which are 3 and 5.
So, the largest odd factor of 6^8 * 10^6 is 3^8 * 5^6, which matches option D.
To find the largest odd factor of a given number, you need to consider the prime factorization of that number. Let's break down the given expression step by step:
6^8 * 10^6
To find the prime factorization of 6^8, let's write it as (2 * 3)^8.
Using the exponent rule, we can rewrite it as 2^8 * 3^8.
For 10^6, we can rewrite it as 2^6 * 5^6, since 10 = 2 * 5.
Now, let's combine both expressions:
(2^8 * 3^8) * (2^6 * 5^6)
By using the multiplication rule, we can multiply the powers of the same base:
2^(8+6) * 3^8 * 5^6
Simplifying the exponent, we have:
2^14 * 3^8 * 5^6
To find the largest odd factor, we want to eliminate the even powers of 2, since they won't contribute to an odd factor.
The largest odd factor will be obtained by writing the expression as:
(2^2 * 2^12) * 3^8 * 5^6
Now, let's calculate the factors:
2^2 = 4 (even)
2^12 = 4096 (even)
3^8 = 6561 (odd)
5^6 = 15625 (odd)
We can see that the largest odd factor is 6561, which is equivalent to 3^8.
Therefore, the correct answer is option D) 3^8 * 5^6.