integer-input-directive.js

.directive('intnum', function () {
    return {
        require: 'ngModel',
        restrict: 'A',
        scope: {
            intnum: '='
        },
        link: function (scope, elem, attr, ctrl) {
            elem.bind('change', function() {
                var value = isNaN(parseInt(ctrl.$viewValue)) ? 1 : parseInt(ctrl.$viewValue);
                var min, max, newValue;

                if(scope.intnum !== undefined) {

                    if(scope.intnum.hasOwnProperty('min') && scope.intnum.hasOwnProperty('max')) {
                        var minimum = parseInt(scope.intnum.min);
                        var maximum = parseInt(scope.intnum.max);

                        min = minimum > maximum ? maximum : minimum;
                        max = maximum < minimum ? minimum : maximum;

                        if(!isNaN(min) && !isNaN(max)) {

                            if(value < min) {
                                value = min;
                            } else if(value > max) {
                                value = max;
                            }
                            
                        } else if (isNaN(min) && !isNaN(max)) {

                            if(value > max) {
                                value = max;
                            }
                            
                        } else if (isNaN(max) && !isNaN(min)) {

                            if(value < min) {
                                value = min;
                            }

                        }

                    } else if (scope.intnum.hasOwnProperty('min')) {

                        min = parseInt(scope.intnum.min);

                        if(!isNaN(min) && value < min) {
                            value = min;
                        }

                    } else if (scope.intnum.hasOwnProperty('max')) {

                        max = parseInt(scope.intnum.max);

                        if(!isNaN(max) && value > max) {
                            value = max;
                        }

                    }
                }

                ctrl.$setViewValue(value.toString());
                ctrl.$render();

            });
        }
    };
});

<input ng-model="age" type="text" class="form-control" intnum="{min: 1}" required />

intnum
intnum=""
intnum="{min: 1}"
intnum="{min: 1, max: 5}"