Q: What are the prime factors of the number 134,332,416?

A: 2, 3, 911

Why are those the prime factors of the number 134,332,416?

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 134,332,416

	134,332,416

2		67,166,208

	2		33,583,104

		2		16,791,552

			2		8,395,776

				2		4,197,888

					2		2,098,944

						2		1,049,472

							2		524,736

								2		262,368

									2		131,184

										2		65,592

											2		32,796

												2		16,398

													2		8,199

														3		2,733

															3		911

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, 911

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 3 x 3 x 911 = 134,332,416

This can also be written as 2¹⁴ x 3² x 911¹ = 134,332,416

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