diff --git a/luhn.go b/luhn.go
index 27bbf7a..300b68a 100644
--- a/luhn.go
+++ b/luhn.go
@@ -2,7 +2,6 @@ package luhn
 
 import (
 	"fmt"
-	"strconv"
 )
 
 type luhnNumber struct {
@@ -16,14 +15,13 @@ func (l luhnNumber) calculateCheckDigit() (luhnNumber, error) {
 		return l, fmt.Errorf("invalid input: number must be positive")
 	}
 
-	strNumbers := strconv.FormatInt(l.baseNumber, 10)
+	temp := l.baseNumber
 	var total int
+	multiplier := 0
 
-	for i, multiplier := len(strNumbers)-1, 0; i >= 0; i-- {
-		digit, err := strconv.Atoi(string(strNumbers[i]))
-		if err != nil {
-			return l, fmt.Errorf("invalid digit at position %d: %v", i, err)
-		}
+	for temp > 0 {
+		digit := int(temp % 10)
+		temp /= 10
 
 		if multiplier%2 == 0 {
 			digit *= 2
@@ -53,12 +51,8 @@ func FullNumber(number int64) (int64, error) {
 		return 0, fmt.Errorf("failed to generate check digit: %v", err)
 	}
 
-	strNumbers := strconv.FormatInt(number, 10) + strconv.Itoa(res.checkDigit)
-
-	finalNumber, err := strconv.ParseInt(strNumbers, 10, 64)
-	if err != nil {
-		return 0, fmt.Errorf("failed to parse final number: %v", err)
-	}
+	// Append check digit arithmetically
+	finalNumber := number*10 + int64(res.checkDigit)
 	return finalNumber, nil
 }
 
@@ -79,16 +73,12 @@ func CheckDigit(number int64) (int, error) {
 
 // IsValid checks if the number is valid according to the Luhn algorithm
 func IsValid(number int64) bool {
-	s := strconv.FormatInt(number, 10)
-	if len(s) < 2 {
+	if number < 10 {
 		return false
 	}
 
-	baseNumberStr := s[:len(s)-1]
-	checkDigitStr := s[len(s)-1:]
-
-	baseNumber, _ := strconv.ParseInt(baseNumberStr, 10, 64)
-	checkDigit, _ := strconv.Atoi(checkDigitStr)
+	checkDigit := int(number % 10)
+	baseNumber := number / 10
 
 	ln := luhnNumber{
 		baseNumber: baseNumber,
diff --git a/luhn_test.go b/luhn_test.go
index ef05808..867e4d1 100644
--- a/luhn_test.go
+++ b/luhn_test.go
@@ -87,3 +87,21 @@ func TestLuhnAlgorithm(t *testing.T) {
 		})
 	}
 }
+
+func BenchmarkCheckDigit(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		CheckDigit(7992739871)
+	}
+}
+
+func BenchmarkFullNumber(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		FullNumber(7992739871)
+	}
+}
+
+func BenchmarkIsValid(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		IsValid(79927398713)
+	}
+}