Q: What are the prime factors of the number 405,463,040?

A: 2, 5, 19, 521

Why are those the prime factors of the number 405,463,040?

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 405,463,040

	405,463,040

2		202,731,520

	2		101,365,760

		2		50,682,880

			2		25,341,440

				2		12,670,720

					2		6,335,360

						2		3,167,680

							2		1,583,840

								2		791,920

									2		395,960

										2		197,980

											2		98,990

												2		49,495

													5		9,899

														19		521

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, 5, 19, 521

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 5 x 19 x 521 = 405,463,040

This can also be written as 2¹³ x 5¹ x 19¹ x 521¹ = 405,463,040

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