Q: What are the prime factors of the number 171,229,184?

A: 2, 7, 1493

Why are those the prime factors of the number 171,229,184?

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 171,229,184

	171,229,184

2		85,614,592

	2		42,807,296

		2		21,403,648

			2		10,701,824

				2		5,350,912

					2		2,675,456

						2		1,337,728

							2		668,864

								2		334,432

									2		167,216

										2		83,608

											2		41,804

												2		20,902

													2		10,451

														7		1,493

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, 7, 1493

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 7 x 1,493 = 171,229,184

This can also be written as 2¹⁴ x 7¹ x 1,493¹ = 171,229,184

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