Study Guides/Maths/Prime Factorization of 2907 – Step by Step Solution
Study Guide · Maths

Prime Factorization of 2907

The prime factorization of 2907 is 3² × 17 × 19. The prime factors of 2907 are 3, 17, and 19. Dividing step by step: 2907 ÷ 3 = 969, 969 ÷ 3 = 323, 323 ÷ 17 = 19 (prime).

Question (Click to Flip)

What is the prime factorization of 2907?

Answer

2907 = 3² × 17 × 19. The prime factors are 3, 17, and 19.

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Key Facts

2907 = 3² × 17 × 19

Prime factors of 2907 are 3, 17, and 19

2907 is divisible by 3 (digit sum = 18, divisible by 3)

2907 ÷ 3 = 969; 969 ÷ 3 = 323; 323 ÷ 17 = 19

2907 has 12 total factors

2907 is an odd composite number

Verification: 9 × 17 × 19 = 2907

Factor pairs include: (3, 969), (9, 323), (17, 171), (19, 153)

Step-by-Step Division Method

Find prime factors of 2907 by dividing by smallest primes:

Step 1: Is 2907 divisible by 2? No (it's odd) Step 2: Is 2907 divisible by 3? Sum of digits = 2+9+0+7 = 18 → divisible by 3 2907 ÷ 3 = 969

Step 3: Is 969 divisible by 3? Sum of digits = 9+6+9 = 24 → divisible by 3 969 ÷ 3 = 323

Step 4: Is 323 divisible by 3? 3+2+3 = 8 → No Step 5: Is 323 divisible by 7? 323 ÷ 7 = 46.1... → No Step 6: Is 323 divisible by 11? 323 ÷ 11 = 29.4... → No Step 7: Is 323 divisible by 13? 323 ÷ 13 = 24.8... → No Step 8: Is 323 divisible by 17? 323 ÷ 17 = 19 → Yes! Step 9: 19 is a prime number.

Result: 2907 = 3 × 3 × 17 × 19 = 3² × 17 × 19

Factor Tree of 2907

  2907
 /    \
3     969
     /   \
    3    323
        /   \
       17    19

Prime factors: 3, 3, 17, 19 Prime factorization: 3² × 17 × 19

Verification: 9 × 17 × 19 = 9 × 323 = 2907 ✓

All Factors of 2907

Using prime factorization 3² × 17 × 19:

All factors of 2907: 1, 3, 9, 17, 19, 51, 153, 171, 323, 969, 2907

Total number of factors = (2+1)(1+1)(1+1) = 3 × 2 × 2 = 12 factors

Factor pairs: 1 × 2907 3 × 969 9 × 323 17 × 171 19 × 153 51 × 57

Questions and Answers

What is the prime factorization of 2907?+

2907 = 3² × 17 × 19. The prime factors are 3, 17, and 19.

How do you find the prime factorization of 2907?+

Divide 2907 by 3 to get 969, divide 969 by 3 to get 323, then divide 323 by 17 to get 19 (prime). So 2907 = 3 × 3 × 17 × 19.

Is 2907 divisible by 3?+

Yes, 2907 is divisible by 3. The sum of digits 2+9+0+7 = 18, which is divisible by 3, so 2907 is also divisible by 3. 2907 ÷ 3 = 969.

How many factors does 2907 have?+

2907 has 12 factors: 1, 3, 9, 17, 19, 51, 153, 171, 323, 969, 2907. Using the formula: (2+1)(1+1)(1+1) = 12.

What are the factor pairs of 2907?+

Factor pairs of 2907: (1,2907), (3,969), (9,323), (17,171), (19,153), (51,57).

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