Question

How to find square root of 768 by prime factorisation

Answer 1

768 is made from three consecutive numbers so it is divisible by 3.

• 768 is a composite number.
• Prime factorization: 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3, which can be written 768 = ($2^8$) x 3
• The exponents in the prime factorization are 8 and 1. Adding one to each and multiplying we get (8 + 1)(1 + 1) = 9 x 2 = 18. Therefore 768 has exactly 18 factors.
• Factors of 768: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
• Factor pairs: 768 = 1 x 768, 2 x 384, 3 x 256, 4 x 192, 6 x 128, 8 x 96, 12 x 64, 16 x 48 or 24 x 32
• Taking the factor pair with the largest square number factor, we get √768 = (√256)(√3) = 16√3 ≈ 27.7128129.