Factor the Modulus

Five Divides Fifty Five

The first divisor with zero remainder reveals both prime factors.

highlighted = computed this step

Five divides the modulus

Trial 5 leaves remainder 0, so it divides n.

55 mod 5=055\bmod{}5=0
The factor rowTrial division rows are recomputed from the public toy RSA modulus.Try small divisors - n=55 factors to 5 x 11trialn mod trialdividesquotientstatus21no-no31no-no43no-no50yes11factor

The other factor appears

Dividing n by 5 gives quotient 11.

55/5=1155/5=11
The factor rowTrial division rows are recomputed from the public toy RSA modulus.Try small divisors - n=55 factors to 5 x 11trialn mod trialdividesquotientstatus21no-no31no-no43no-no50yes11factor

Multiply back to check

The factors multiply back to n: 5 times 11 equals 55.

5⋅11=555\cdot11=55
The factor rowTrial division rows are recomputed from the public toy RSA modulus.Try small divisors - n=55 factors to 5 x 11trialn mod trialdividesquotientstatus21no-no31no-no43no-no50yes11factor

Summary

The tiny modulus has been factored into p=5 and q=11.

p,q=5,11p,q=5,11
The factor rowTrial division rows are recomputed from the public toy RSA modulus.Try small divisors - n=55 factors to 5 x 11trialn mod trialdividesquotientstatus21no-no31no-no43no-no50yes11factor