diff --git a/openapi3/schema.go b/openapi3/schema.go
index 1be5d8385..a7e845f79 100644
--- a/openapi3/schema.go
+++ b/openapi3/schema.go
@@ -7,6 +7,7 @@ import (
 	"errors"
 	"fmt"
 	"math"
+	"math/big"
 	"regexp"
 	"strconv"
 	"strings"
@@ -164,16 +165,22 @@ func NewFloat64Schema() *Schema {
 	}
 }
 
+func NewIntegerSchema() *Schema {
+	return &Schema{
+		Type: "integer",
+	}
+}
+
 func NewInt32Schema() *Schema {
 	return &Schema{
-		Type:   "number",
+		Type:   "integer",
 		Format: "int32",
 	}
 }
 
 func NewInt64Schema() *Schema {
 	return &Schema{
-		Type:   "number",
+		Type:   "integer",
 		Format: "int64",
 	}
 }
@@ -432,14 +439,31 @@ func (schema *Schema) validate(c context.Context, stack []*Schema) error {
 	schemaType := schema.Type
 	switch schemaType {
 	case "":
-	case "integer", "long", "float", "double":
+	case "number":
+		if format := schema.Format; len(format) > 0 {
+			switch format {
+			case "float", "double":
+			default:
+				return fmt.Errorf("Unsupported 'format' value '%v", format)
+			}
+		}
+	case "integer":
+		if format := schema.Format; len(format) > 0 {
+			switch format {
+			case "int32", "int64":
+			default:
+				return fmt.Errorf("Unsupported 'format' value '%v", format)
+			}
+		}
 	case "string":
-	case "byte":
-	case "binary":
+		if format := schema.Format; len(format) > 0 {
+			switch format {
+			case "byte", "binary", "date", "dateTime", "password":
+			default:
+				return fmt.Errorf("Unsupported 'format' value '%v", format)
+			}
+		}
 	case "boolean":
-	case "date":
-	case "dateTime":
-	case "password":
 	case "array":
 		if schema.Items == nil {
 			return errors.New("When schema type is 'array', schema 'items' must be non-null")
@@ -689,7 +713,7 @@ func (schema *Schema) visitJSONNumber(value float64, fast bool) error {
 	if math.IsInf(value, 0) {
 		return ErrSchemaInputInf
 	}
-	if err := schema.validateTypeListAllows("number", fast); err != nil {
+	if err := schema.validateJSONNumber(value, fast); err != nil {
 		return err
 	}
 
@@ -1084,6 +1108,14 @@ func (schema *Schema) visitJSONObject(value map[string]interface{}, fast bool) e
 	return nil
 }
 
+func (schema *Schema) validateJSONNumber(value float64, fast bool) error {
+	bigFloat := big.NewFloat(value)
+	if bigFloat.IsInt() && schema.TypesContains("integer") {
+		return nil
+	}
+	return schema.validateTypeListAllows("number", fast)
+}
+
 func (schema *Schema) validateTypeListAllows(value string, fast bool) error {
 	schemaType := schema.Type
 	if schemaType != "" {
diff --git a/openapi3/schema_test.go b/openapi3/schema_test.go
index bf6291532..fb26de498 100644
--- a/openapi3/schema_test.go
+++ b/openapi3/schema_test.go
@@ -136,6 +136,34 @@ var schemaExamples = []schemaExample{
 		},
 	},
 
+	{
+		Title: "INTEGER",
+		Schema: openapi3.NewInt64Schema().
+			WithMin(2).
+			WithMax(5),
+		Serialization: map[string]interface{}{
+			"type":    "integer",
+			"format":  "int64",
+			"minimum": 2,
+			"maximum": 5,
+		},
+		AllValid: []interface{}{
+			2,
+			5,
+		},
+		AllInvalid: []interface{}{
+			nil,
+			false,
+			true,
+			1,
+			6,
+			3.5,
+			"",
+			[]interface{}{},
+			map[string]interface{}{},
+		},
+	},
+
 	{
 		Title: "STRING",
 		Schema: openapi3.NewStringSchema().
@@ -510,3 +538,79 @@ var schemaExamples = []schemaExample{
 		},
 	},
 }
+
+type schemaTypeExample struct {
+	Title      string
+	Schema     *openapi3.Schema
+	AllValid   []string
+	AllInvalid []string
+}
+
+func TestTypes(t *testing.T) {
+	for _, example := range typeExamples {
+		t.Run(example.Title, testType(t, example))
+	}
+}
+
+func testType(t *testing.T, example schemaTypeExample) func(*testing.T) {
+	return func(t *testing.T) {
+		schema := example.Schema
+		for _, typ := range example.AllValid {
+			err := validateType(t, schema, typ)
+			require.NoError(t, err)
+		}
+		for _, typ := range example.AllInvalid {
+			err := validateType(t, schema, typ)
+			require.Error(t, err)
+		}
+	}
+}
+
+func validateType(t *testing.T, schema *openapi3.Schema, typ string) error {
+	schema.WithFormat(typ)
+	return schema.Validate(nil)
+}
+
+var typeExamples = []schemaTypeExample{
+	{
+		Title:  "STRING",
+		Schema: openapi3.NewStringSchema(),
+		AllValid: []string{
+			"",
+			"byte",
+			"binary",
+			"date",
+			"dateTime",
+			"password",
+		},
+		AllInvalid: []string{
+			"unsupported",
+		},
+	},
+
+	{
+		Title:  "NUMBER",
+		Schema: openapi3.NewFloat64Schema(),
+		AllValid: []string{
+			"",
+			"float",
+			"double",
+		},
+		AllInvalid: []string{
+			"unsupported",
+		},
+	},
+
+	{
+		Title:  "INTEGER",
+		Schema: openapi3.NewIntegerSchema(),
+		AllValid: []string{
+			"",
+			"int32",
+			"int64",
+		},
+		AllInvalid: []string{
+			"unsupported",
+		},
+	},
+}
diff --git a/openapi3gen/openapi3gen.go b/openapi3gen/openapi3gen.go
index 1a982257f..4a80405ba 100644
--- a/openapi3gen/openapi3gen.go
+++ b/openapi3gen/openapi3gen.go
@@ -116,7 +116,7 @@ func (g *Generator) generateWithoutSaving(parents []*jsoninfo.TypeInfo, t reflec
 	case reflect.Int,
 		reflect.Int8, reflect.Int16, reflect.Int32, reflect.Int64,
 		reflect.Uint8, reflect.Uint16, reflect.Uint32, reflect.Uint64:
-		schema.Type = "number"
+		schema.Type = "integer"
 		schema.Format = "int64"
 
 	case reflect.Float32, reflect.Float64:
diff --git a/openapi3gen/openapi3gen_test.go b/openapi3gen/openapi3gen_test.go
index 83c38433d..d94cfce9f 100644
--- a/openapi3gen/openapi3gen_test.go
+++ b/openapi3gen/openapi3gen_test.go
@@ -61,11 +61,11 @@ const expectedSimple = `
       "type": "boolean"
     },
     "int": {
-      "type": "number",
+      "type": "integer",
       "format": "int64"
     },
     "int64": {
-      "type": "number",
+      "type": "integer",
       "format": "int64"
     },
     "float64": {