Q: What are the prime factors of the number 232,423,424?

A: 2, 41, 173

Why are those the prime factors of the number 232,423,424?

Prime factors are the prime numbers that can be multipled together to equal the original number. You find the factors by dividing by prime numbers. It is best shown by creating a Factor Tree.

Factor Tree for the number 232,423,424

	232,423,424

2		116,211,712

	2		58,105,856

		2		29,052,928

			2		14,526,464

				2		7,263,232

					2		3,631,616

						2		1,815,808

							2		907,904

								2		453,952

									2		226,976

										2		113,488

											2		56,744

												2		28,372

													2		14,186

														2		7,093

															41		173

The numbers in bold above are the prime factors. If there are multiples, you only count them one time. This leads us to our prime factors of:

2, 41, 173

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 41 x 173 = 232,423,424

This can also be written as 2¹⁵ x 41¹ x 173¹ = 232,423,424

If you would like to know more, or need additional explanation, please review our prime factorization explanation.