diff --git a/formulaic/parser/parser.py b/formulaic/parser/parser.py
index e030594..2871926 100644
--- a/formulaic/parser/parser.py
+++ b/formulaic/parser/parser.py
@@ -5,6 +5,8 @@
 from dataclasses import dataclass, field
 from typing import List, Iterable, Sequence, Tuple, Union, cast
 
+from formulaic.parser.types.factor import Factor
+
 from .algos.tokenize import tokenize
 from .types import (
     FormulaParser,
@@ -114,6 +116,52 @@ def get_tokens(self, formula: str) -> Iterable[Token]:
 
         return tokens
 
+    def get_terms(self, formula: str) -> Structured[List[Term]]:
+        """
+        Assemble the `Term` instances for a formula string. Depending on the
+        operators involved, this may be an iterable of `Term` instances, or
+        an iterable of iterables of `Term`s, etc.
+
+        This implementation also verifies that the formula is well-formed, in
+        that it does not have any literals apart from 1 or numeric scaling of
+        other terms.
+
+        Args:
+            formula: The formula for which an AST should be generated.
+        """
+        terms = super().get_terms(formula)
+
+        def check_terms(terms: Iterable[Term]) -> None:
+            for term in terms:
+                if len(term.factors) == 1:
+                    factor = term.factors[0]
+                    if (
+                        factor.eval_method is Factor.EvalMethod.LITERAL
+                        and factor.expr != "1"
+                    ):
+                        raise exc_for_token(
+                            factor.token or Token(),
+                            "Numeric literals other than `1` can only be used "
+                            "to scale other terms. (tip: Use `:` rather than "
+                            "`*` when scaling terms)"
+                            if factor.expr.replace(".", "", 1).isnumeric()
+                            else "String literals are not valid in formulae.",
+                        )
+                else:
+                    for factor in term.factors:
+                        if (
+                            factor.eval_method is Factor.EvalMethod.LITERAL
+                            and not factor.expr.replace(".", "", 1).isnumeric()
+                        ):
+                            raise exc_for_token(
+                                factor.token or Token(),
+                                "String literals are not valid in formulae.",
+                            )
+
+        terms._map(check_terms)
+
+        return terms
+
 
 class DefaultOperatorResolver(OperatorResolver):
     """
diff --git a/tests/parser/test_parser.py b/tests/parser/test_parser.py
index 315bd2f..44e1ad5 100644
--- a/tests/parser/test_parser.py
+++ b/tests/parser/test_parser.py
@@ -73,6 +73,8 @@
     "(a+b)**2": ["1", "a", "a:b", "b"],
     "(a+b)^2": ["1", "a", "a:b", "b"],
     "(a+b)**3": ["1", "a", "a:b", "b"],
+    "50:a": ["1", "50:a"],
+    "1 * a": ["1", "a", "1:a"],
     # Nested products
     "a/b": ["1", "a", "a:b"],
     "(b+a)/c": ["1", "b", "a", "b:a:c"],
@@ -162,6 +164,32 @@ def test_long_formula(self):
         terms = PARSER_NO_INTERCEPT.get_terms(expr)
         assert {str(term) for term in terms} == names
 
+    def test_invalid_literals(self):
+        with pytest.raises(
+            FormulaSyntaxError,
+            match=re.escape(
+                "Numeric literals other than `1` can only be used to scale other terms."
+            ),
+        ):
+            PARSER.get_terms("50")
+        with pytest.raises(
+            FormulaSyntaxError,
+            match=re.escape("String literals are not valid in formulae."),
+        ):
+            PARSER.get_terms("'asd'")
+        with pytest.raises(
+            FormulaSyntaxError,
+            match=re.escape(
+                "Numeric literals other than `1` can only be used to scale other terms."
+            ),
+        ):
+            PARSER.get_terms("50*a")
+        with pytest.raises(
+            FormulaSyntaxError,
+            match=re.escape("String literals are not valid in formulae."),
+        ):
+            PARSER.get_terms("'asd':a")
+
 
 class TestDefaultOperatorResolver:
     @pytest.fixture