Q: What are the prime factors of the number 233,521,152?

A: 2, 3, 4751

Why are those the prime factors of the number 233,521,152?

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 233,521,152

	233,521,152

2		116,760,576

	2		58,380,288

		2		29,190,144

			2		14,595,072

				2		7,297,536

					2		3,648,768

						2		1,824,384

							2		912,192

								2		456,096

									2		228,048

										2		114,024

											2		57,012

												2		28,506

													2		14,253

														3		4,751

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, 3, 4751

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 3 x 4,751 = 233,521,152

This can also be written as 2¹⁴ x 3¹ x 4,751¹ = 233,521,152

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