Prime Factorization of 35,280

What Is the Prime Factorization of 35,280?

35,280 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7, which is written 2⁴ × 3² × 5 × 7² with exponents. Every number in that product is prime, so it cannot be broken down any further. The prime factors of 35,280 are 2, 3, 5, 7.

Handwritten notebook page showing the division ladder for the prime factorization of 35,280 — Division ladder for 35,280: 35,280 = 2⁴ × 3² × 5 × 7².

Division Ladder for 35,280

Divide by the smallest prime that goes in, write the answer, and repeat until you reach 1.

35,280 ÷ 2 = 17,640
17,640 ÷ 2 = 8,820
8,820 ÷ 2 = 4,410
4,410 ÷ 2 = 2,205
2,205 ÷ 3 = 735
735 ÷ 3 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

The numbers in bold are the prime factors: 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7.

Write It with Exponents

2 appears 4 times, written 2⁴
3 appears 2 times, written 3²
5 appears 1 time, written 5
7 appears 2 times, written 7²

Put together: 35,280 = 2⁴ × 3² × 5 × 7².

Check by Multiplying Back

2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7 = 35,280. It matches the number we started with, so the factorization is right.

Count the Factors of 35,280

Add 1 to each exponent and multiply: (4 + 1) × (2 + 1) × (1 + 1) × (2 + 1) = 90. So 35,280 has 90 factors:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 49, 56, 60, 63, 70, 72, 80, 84, 90, 98, 105, 112, 120, 126, 140, 144, 147, 168, 180, 196, 210, 240, 245, 252, 280, 294, 315, 336, 360, 392, 420, 441, 490, 504, 560, 588, 630, 720, 735, 784, 840, 882, 980, 1,008, 1,176, 1,260, 1,470, 1,680, 1,764, 1,960, 2,205, 2,352, 2,520, 2,940, 3,528, 3,920, 4,410, 5,040, 5,880, 7,056, 8,820, 11,760, 17,640, 35,280

Prime or composite?

35,280 is composite, because it has more than two factors. Try another number in the Prime Factorization Calculator.

Prime Factorization of 35,280: FAQs

What is the prime factorization of 35,280?

35,280 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 7 = 2⁴ × 3² × 5 × 7².

What are the prime factors of 35,280?

The prime factors of 35,280 are 2, 3, 5, 7.

Is 35,280 a prime or composite number?

35,280 is composite. It has 90 factors, and anything with more than two factors is not prime.

How many factors does 35,280 have?

35,280 has 90 factors: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 49, 56, 60, 63, 70, 72, 80, 84, 90, 98, 105, 112, 120, 126, 140, 144, 147, 168, 180, 196, 210, 240, 245, 252, 280, 294, 315, 336, 360, 392, 420, 441, 490, 504, 560, 588, 630, 720, 735, 784, 840, 882, 980, 1,008, 1,176, 1,260, 1,470, 1,680, 1,764, 1,960, 2,205, 2,352, 2,520, 2,940, 3,528, 3,920, 4,410, 5,040, 5,880, 7,056, 8,820, 11,760, 17,640, 35,280. Add 1 to each exponent and multiply: (4 + 1) × (2 + 1) × (1 + 1) × (2 + 1) = 90.