If both 7^2 and 2^2 are the factors of the number (a x 4^3 x 5^5 x 17^2), then what is the smallest possible value of a?
Answers
Step-by-step explanation:
Now, we can express the ones on the right in simpler terms.
11^2 * 3^2 = a* 2^6 * 2^2* 3^2 * 13^11
We cancel out the 3^2 on both sides.
11^2= a 2^8 * 13^11
And use division to get the result.
a = 11^2/(2^8 * 13^11)
a = 2,63735... *10^-13
You can calculate it yourself, but it should be the smallest possible value for a.
Given : both 7² and 2² are the factors of the number (a x 4³ x 5⁵ x 17²)
To Find : smallest possible value of a
Solution:
a x 4³ x 5⁵ x 17²
= a x (2²)³ x 5⁵ x 17²
= a x 2⁶ x 5⁵ x 17²
= a x 2²⁺⁴ x 5⁵ x 17²
= a x 2² x 2⁴ x 5⁵ x 17²
both 7² and 2² are the factors of the number
2² is already present
Hence a must contain a factor 7²
Smallest possible value of a is 7² = 49
Smallest possible value of a = 49
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