Question

If 1176 = 2^a ×3^b×7^c
Find the value of a, b, c

Answer 1

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Answer 2

Answer:

a = 3 , b = 1 , c = 2

Explanation:

_____________________

Fundamental theorem of arithmetic:

Every composite number can be expressed as product of prime unique way.

__________________________

Resolve 1176 into product of

prime .

2| 1176

_________

2| 588

_________

2| 294

_________

3| 147

_________

7| 49

_________

*****7

1176 = 2³ × 3¹ × 7²

Now,

$1176 = 2^{a}\times3^{b}\times 7^{c}$

$\implies 2^{3}\times 3^{1}\times7^{2} = 2^{a}\times3^{b}\times 7^{c}$

Compare both sides, we get

a=3 , b = 1 , c = 2

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