diff --git a/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs b/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
index 5030c6233f6..f54ddd9f4d4 100644
--- a/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
+++ b/compiler/noirc_evaluator/src/ssa/acir_gen/acir_ir/acir_variable.rs
@@ -563,13 +563,36 @@ impl AcirContext {
         // lhs = rhs * q + r
         //
         // If predicate is zero, `q_witness` and `r_witness` will be 0
+        let zero = self.add_constant(FieldElement::zero());
+        if self.var_to_expression(predicate)?.is_zero() {
+            return Ok((zero, zero));
+        }
+
+        match (self.var_to_expression(lhs)?.to_const(), self.var_to_expression(rhs)?.to_const()) {
+            // If `lhs` and `rhs` are known constants then we can calculate the result at compile time.
+            // `rhs` must be non-zero.
+            (Some(lhs_const), Some(rhs_const)) if rhs_const != FieldElement::zero() => {
+                let quotient = lhs_const.to_u128() / rhs_const.to_u128();
+                let remainder = lhs_const.to_u128() - quotient * rhs_const.to_u128();
+
+                let quotient_var = self.add_constant(FieldElement::from(quotient));
+                let remainder_var = self.add_constant(FieldElement::from(remainder));
+                return Ok((quotient_var, remainder_var));
+            }
+
+            // If `rhs` is one then the division is a noop.
+            (_, Some(rhs_const)) if rhs_const == FieldElement::one() => {
+                return Ok((lhs, zero));
+            }
+
+            _ => (),
+        }
 
         // Check that we the rhs is not zero.
         // Otherwise, when executing the brillig quotient we may attempt to divide by zero, causing a VM panic.
         //
         // When the predicate is 0, the equation always passes.
         // When the predicate is 1, the rhs must not be 0.
-        let zero = self.add_constant(FieldElement::zero());
         let one = self.add_constant(FieldElement::one());
 
         let rhs_expr = self.var_to_expression(rhs)?;
diff --git a/tooling/nargo_cli/tests/acir_artifacts/conditional_1/target/acir.gz b/tooling/nargo_cli/tests/acir_artifacts/conditional_1/target/acir.gz
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diff --git a/tooling/nargo_cli/tests/acir_artifacts/conditional_1/target/witness.gz b/tooling/nargo_cli/tests/acir_artifacts/conditional_1/target/witness.gz
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diff --git a/tooling/nargo_cli/tests/acir_artifacts/simple_shield/target/acir.gz b/tooling/nargo_cli/tests/acir_artifacts/simple_shield/target/acir.gz
index 0600c1dfc78..9a9f3a76992 100644
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diff --git a/tooling/nargo_cli/tests/acir_artifacts/slice_dynamic_index/target/acir.gz b/tooling/nargo_cli/tests/acir_artifacts/slice_dynamic_index/target/acir.gz
index 70fa092b84d..30b5d36a2e3 100644
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diff --git a/tooling/nargo_cli/tests/acir_artifacts/slice_dynamic_index/target/witness.gz b/tooling/nargo_cli/tests/acir_artifacts/slice_dynamic_index/target/witness.gz
index a7846969bd8..1cbd7129bb0 100644
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diff --git a/tooling/nargo_cli/tests/acir_artifacts/slices/target/acir.gz b/tooling/nargo_cli/tests/acir_artifacts/slices/target/acir.gz
index b2ec8995408..70a32bccf6f 100644
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