diff --git a/clippy_lints/src/operators/arithmetic_side_effects.rs b/clippy_lints/src/operators/arithmetic_side_effects.rs
index f9108145cdb..a687c7d29b5 100644
--- a/clippy_lints/src/operators/arithmetic_side_effects.rs
+++ b/clippy_lints/src/operators/arithmetic_side_effects.rs
@@ -1,24 +1,20 @@
 use super::ARITHMETIC_SIDE_EFFECTS;
 use clippy_utils::consts::{constant, constant_simple, Constant};
 use clippy_utils::diagnostics::span_lint;
+use clippy_utils::ty::type_diagnostic_name;
 use clippy_utils::{expr_or_init, is_from_proc_macro, is_lint_allowed, peel_hir_expr_refs, peel_hir_expr_unary};
 use rustc_data_structures::fx::{FxHashMap, FxHashSet};
 use rustc_lint::{LateContext, LateLintPass};
 use rustc_middle::ty::Ty;
 use rustc_session::impl_lint_pass;
 use rustc_span::source_map::{Span, Spanned};
+use rustc_span::symbol::sym;
 use rustc_span::Symbol;
 use {rustc_ast as ast, rustc_hir as hir};
 
-const HARD_CODED_ALLOWED_BINARY: &[[&str; 2]] = &[
-    ["f32", "f32"],
-    ["f64", "f64"],
-    ["std::num::Saturating", "*"],
-    ["std::num::Wrapping", "*"],
-    ["std::string::String", "str"],
-];
+const HARD_CODED_ALLOWED_BINARY: &[[&str; 2]] = &[["f32", "f32"], ["f64", "f64"], ["std::string::String", "str"]];
 const HARD_CODED_ALLOWED_UNARY: &[&str] = &["f32", "f64", "std::num::Saturating", "std::num::Wrapping"];
-const INTEGER_METHODS: &[&str] = &["saturating_div", "wrapping_div", "wrapping_rem", "wrapping_rem_euclid"];
+const INTEGER_METHODS: &[Symbol] = &[sym::saturating_div, sym::wrapping_div, sym::wrapping_rem, sym::wrapping_rem_euclid];
 
 #[derive(Debug)]
 pub struct ArithmeticSideEffects {
@@ -53,7 +49,7 @@ impl ArithmeticSideEffects {
             allowed_unary,
             const_span: None,
             expr_span: None,
-            integer_methods: INTEGER_METHODS.iter().map(|el| Symbol::intern(el)).collect(),
+            integer_methods: INTEGER_METHODS.iter().copied().collect(),
         }
     }
 
@@ -86,6 +82,38 @@ impl ArithmeticSideEffects {
         self.allowed_unary.contains(ty_string_elem)
     }
 
+    /// Verifies built-in types that have specific allowed operations
+    fn has_specific_allowed_type_and_operation(
+        cx: &LateContext<'_>,
+        lhs_ty: Ty<'_>,
+        op: &Spanned<hir::BinOpKind>,
+        rhs_ty: Ty<'_>,
+    ) -> bool {
+        let is_div_or_rem = matches!(op.node, hir::BinOpKind::Div | hir::BinOpKind::Rem);
+        let is_non_zero_u = |symbol: Option<Symbol>| {
+            matches!(
+                symbol,
+                Some(sym::NonZeroU128 | sym::NonZeroU16 | sym::NonZeroU32 | sym::NonZeroU64 | sym::NonZeroU8 | sym::NonZeroUsize)
+            )
+        };
+        let is_sat_or_wrap = |ty: Ty<'_>| {
+            let is_sat = type_diagnostic_name(cx, ty) == Some(sym::Saturating);
+            let is_wrap = type_diagnostic_name(cx, ty) == Some(sym::Wrapping);
+            is_sat || is_wrap
+        };
+
+        // If the RHS is NonZeroU*, then division or module by zero will never occur
+        if is_non_zero_u(type_diagnostic_name(cx, rhs_ty)) && is_div_or_rem {
+            return true;
+        }
+        // `Saturation` and `Wrapping` can overflow if the RHS is zero in a division or module
+        if is_sat_or_wrap(lhs_ty) {
+            return !is_div_or_rem;
+        }
+
+        false
+    }
+
     // For example, 8i32 or &i64::MAX.
     fn is_integral(ty: Ty<'_>) -> bool {
         ty.peel_refs().is_integral()
@@ -147,6 +175,9 @@ impl ArithmeticSideEffects {
         if self.has_allowed_binary(lhs_ty, rhs_ty) {
             return;
         }
+        if Self::has_specific_allowed_type_and_operation(cx, lhs_ty, op, rhs_ty) {
+            return;
+        }
         let has_valid_op = if Self::is_integral(lhs_ty) && Self::is_integral(rhs_ty) {
             if let hir::BinOpKind::Shl | hir::BinOpKind::Shr = op.node {
                 // At least for integers, shifts are already handled by the CTFE
diff --git a/tests/ui/arithmetic_side_effects.rs b/tests/ui/arithmetic_side_effects.rs
index 8485b3eab71..def30f5903d 100644
--- a/tests/ui/arithmetic_side_effects.rs
+++ b/tests/ui/arithmetic_side_effects.rs
@@ -15,7 +15,7 @@
 
 extern crate proc_macro_derive;
 
-use core::num::{Saturating, Wrapping};
+use core::num::{NonZeroUsize, Saturating, Wrapping};
 
 const ONE: i32 = 1;
 const ZERO: i32 = 0;
@@ -493,4 +493,32 @@ pub fn issue_11262() {
     let _ = 2 / zero;
 }
 
+pub fn issue_11392() {
+    fn example_div(unsigned: usize, nonzero_unsigned: NonZeroUsize) -> usize {
+        unsigned / nonzero_unsigned
+    }
+
+    fn example_rem(unsigned: usize, nonzero_unsigned: NonZeroUsize) -> usize {
+        unsigned % nonzero_unsigned
+    }
+
+    let (unsigned, nonzero_unsigned) = (0, NonZeroUsize::new(1).unwrap());
+    example_div(unsigned, nonzero_unsigned);
+    example_rem(unsigned, nonzero_unsigned);
+}
+
+pub fn issue_11393() {
+    fn example_div(x: Wrapping<i32>, maybe_zero: Wrapping<i32>) -> Wrapping<i32> {
+        x / maybe_zero
+    }
+
+    fn example_rem(x: Wrapping<i32>, maybe_zero: Wrapping<i32>) -> Wrapping<i32> {
+        x % maybe_zero
+    }
+
+    let [x, maybe_zero] = [1, 0].map(Wrapping);
+    example_div(x, maybe_zero);
+    example_rem(x, maybe_zero);
+}
+
 fn main() {}
diff --git a/tests/ui/arithmetic_side_effects.stderr b/tests/ui/arithmetic_side_effects.stderr
index e9a626643ff..7f490748160 100644
--- a/tests/ui/arithmetic_side_effects.stderr
+++ b/tests/ui/arithmetic_side_effects.stderr
@@ -702,5 +702,17 @@ error: arithmetic operation that can potentially result in unexpected side-effec
 LL |     10 / a
    |     ^^^^^^
 
-error: aborting due to 117 previous errors
+error: arithmetic operation that can potentially result in unexpected side-effects
+  --> $DIR/arithmetic_side_effects.rs:512:9
+   |
+LL |         x / maybe_zero
+   |         ^^^^^^^^^^^^^^
+
+error: arithmetic operation that can potentially result in unexpected side-effects
+  --> $DIR/arithmetic_side_effects.rs:516:9
+   |
+LL |         x % maybe_zero
+   |         ^^^^^^^^^^^^^^
+
+error: aborting due to 119 previous errors