Q: What are the prime factors of the number 10,035,200?

A: 2, 5, 7

Why are those the prime factors of the number 10,035,200?

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 10,035,200

	10,035,200

2		5,017,600

	2		2,508,800

		2		1,254,400

			2		627,200

				2		313,600

					2		156,800

						2		78,400

							2		39,200

								2		19,600

									2		9,800

										2		4,900

											2		2,450

												2		1,225

													5		245

														5		49

															7		7

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, 7

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 5 x 7 x 7 = 10,035,200

This can also be written as 2¹³ x 5² x 7² = 10,035,200

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