Theorem : Let p be a prime number. If p divides a² , (where a is a positive integer), then p divides aLet say prime factors of a area = p₁ , p₂ , p₃ ........., pₓ where p₁ to pₓ are prime numbera = (p₁ × p₂ × p₃ ×.........× pₓ)a² = (p₁ × p₂ × p₃ ×.........× pₓ) (p₁ × p₂ × p₃ ×.........× pₓ)if p divides a² then it is one of (p₁ × p₂ × p₃ ×.........× pₓ)as a = (p₁ × p₂ × p₃ ×.........× pₓ) so p divides aVerification forp = 2, p = 5 and for a square = 1, 4, 9, 25, 36, 49, 64 and 81.2 is factor of 4 , 36 & 642 is factor of 2 , 6 & 85 is factor of 255 is a factor of 5 also
