Q: What are the prime factors of the number 332,310,528?

A: 2, 3, 11, 149

Why are those the prime factors of the number 332,310,528?

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 332,310,528

	332,310,528

2		166,155,264

	2		83,077,632

		2		41,538,816

			2		20,769,408

				2		10,384,704

					2		5,192,352

						2		2,596,176

							2		1,298,088

								2		649,044

									2		324,522

										2		162,261

											3		54,087

												3		18,029

													11		1,639

														11		149

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, 11, 149

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 3 x 3 x 11 x 11 x 149 = 332,310,528

This can also be written as 2¹¹ x 3² x 11² x 149¹ = 332,310,528

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