diff --git a/cmd/primitiveRoot.go b/cmd/primitiveRoot.go
index 04f969b..4f65cba 100644
--- a/cmd/primitiveRoot.go
+++ b/cmd/primitiveRoot.go
@@ -40,6 +40,17 @@ func totient(n *big.Int) *big.Int {
 	return total
 }
 
+func multiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {
+	e := new(big.Int).Set(g)
+	var k *big.Int
+	for k = big.NewInt(1); e.Cmp(big.NewInt(1)) != 0; k.Add(k, big.NewInt(1)) {
+		e.Mul(e, g)
+		e.Mod(e, modulus)
+	}
+
+	return k
+}
+
 func computeNaive(modulus *big.Int) (*big.Int, error) {
 	if modulus.Cmp(big.NewInt(1)) == 0 {
 		return big.NewInt(0), nil
@@ -53,14 +64,8 @@ func computeNaive(modulus *big.Int) (*big.Int, error) {
 			continue
 		}
 
-		e := new(big.Int).Set(g)
-		var k *big.Int
-		for k = big.NewInt(1); e.Cmp(big.NewInt(1)) != 0; k.Add(k, big.NewInt(1)) {
-			e.Mul(e, g)
-			e.Mod(e, modulus)
-		}
-
-		if k.Cmp(phi) == 0 {
+		order := multiplicativeOrder(g, modulus)
+		if order.Cmp(phi) == 0 {
 			return g, nil
 		}
 	}