Q: What are the prime factors of the number 210,100,224?

A: 2, 3, 83, 103

Why are those the prime factors of the number 210,100,224?

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 210,100,224

	210,100,224

2		105,050,112

	2		52,525,056

		2		26,262,528

			2		13,131,264

				2		6,565,632

					2		3,282,816

						2		1,641,408

							2		820,704

								2		410,352

									2		205,176

										2		102,588

											2		51,294

												2		25,647

													3		8,549

														83		103

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, 83, 103

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 3 x 83 x 103 = 210,100,224

This can also be written as 2¹³ x 3¹ x 83¹ x 103¹ = 210,100,224

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