Q: What are the prime factors of the number 105,611,264?

A: 2, 11, 293

Why are those the prime factors of the number 105,611,264?

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 105,611,264

	105,611,264

2		52,805,632

	2		26,402,816

		2		13,201,408

			2		6,600,704

				2		3,300,352

					2		1,650,176

						2		825,088

							2		412,544

								2		206,272

									2		103,136

										2		51,568

											2		25,784

												2		12,892

													2		6,446

														2		3,223

															11		293

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, 11, 293

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 11 x 293 = 105,611,264

This can also be written as 2¹⁵ x 11¹ x 293¹ = 105,611,264

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