diff --git a/bigint/bigint_nonjs.mbt b/bigint/bigint_nonjs.mbt
index 8ae12703b..4bcd57691 100644
--- a/bigint/bigint_nonjs.mbt
+++ b/bigint/bigint_nonjs.mbt
@@ -384,7 +384,15 @@ pub impl Mul for BigInt with fn mul(self : BigInt, other : BigInt) -> BigInt {
   if self.is_zero() || other.is_zero() {
     return zero
   }
-  let ret = if self.len < karatsuba_threshold || other.len < karatsuba_threshold {
+  // Specialize the (n-limb) x (1-limb) case. Factorial-style chains hit
+  // this on every multiplication, and the general grade-school loop has
+  // a per-i branch on `j < other_len` plus carry propagation overhead
+  // that disappears here.
+  let ret = if other.len == 1 {
+    self.mul_single_limb(other.limbs[0])
+  } else if self.len == 1 {
+    other.mul_single_limb(self.limbs[0])
+  } else if self.len < karatsuba_threshold || other.len < karatsuba_threshold {
     self.grade_school_mul(other)
   } else {
     self.karatsuba_mul(other)
@@ -392,6 +400,32 @@ pub impl Mul for BigInt with fn mul(self : BigInt, other : BigInt) -> BigInt {
   { ..ret, sign: if self.sign == other.sign { Positive } else { Negative } }
 }
 
+///|
+/// Multiply the magnitude of `self` by a single radix-limb `x`. Returns
+/// a `Positive`-signed result regardless of `self.sign` — the caller in
+/// `Mul::mul` overwrites `sign` with the correct combined sign. This
+/// matches the convention of the other magnitude-only multiply helpers
+/// (`grade_school_mul`, `karatsuba_mul`). Do not call directly when a
+/// signed product is needed.
+fn BigInt::mul_single_limb(self : BigInt, x : UInt) -> BigInt {
+  let n = self.len
+  let limbs = FixedArray::make(n + 1, 0U)
+  let xq = x.to_uint64()
+  let mut carry = 0UL
+  for i in 0..<n {
+    let product = self.limbs[i].to_uint64() * xq + carry
+    limbs[i] = (product & radix_mask).to_uint()
+    carry = product >> radix_bit_len
+  }
+  let len = if carry == 0UL {
+    n
+  } else {
+    limbs[n] = carry.to_uint()
+    n + 1
+  }
+  { limbs, sign: Positive, len }
+}
+
 // Simplest way to multiply two BigInts.
 
 ///|