Question

Find the prime factorization of 3,240

Answer 1

 

3,240 =

= 324 × 10 =

= 4 × 81 × 10 =

= 2^2 × 3^4 × 2 × 5 =

= 2^3 × 3^4 × 5

Answer 2

Answer:

Answer:  3240 = 2^3×3^4×5

Factor the following integer:

3240

The last digit of 3240 is 0, which means it is even. Therefore 3240 is divisible by 2:

3240 = 2 1620:

3240 = 2×1620

The last digit of 1620 is 0, which means it is even. Therefore 1620 is divisible by 2:

1620 = 2 810:

3240 = 2×2×810

The last digit of 810 is 0, which means it is even. Therefore 810 is divisible by 2:

810 = 2 405:

3240 = 2×2×2×405

405 is not divisible by 2 since 405 is odd and 2 is even:

3240 = 2×2×2×405 (405 is not divisible by 2)

The sum of the digits of 405 is 4 + 0 + 5 = 9, which is divisible by 3. This means 405 is divisible by 3:

405 = 3 135:

3240 = 2×2×2×3×135 (135 is not divisible by 2 since 405 is not)

The sum of the digits of 135 is 1 + 3 + 5 = 9, which is divisible by 3. This means 135 is divisible by 3:

135 = 3 45:

3240 = 2×2×2×3×3×45 (45 is not divisible by 2 since 135 is not)

The sum of the digits of 45 is 4 + 5 = 9, which is divisible by 3. This means 45 is divisible by 3:

45 = 3 15:

3240 = 2×2×2×3×3×3×15 (15 is not divisible by 2 since 45 is not)

The sum of the digits of 15 is 1 + 5 = 6, which is divisible by 3. This means 15 is divisible by 3:

15 = 3 5:

3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 since 15 is not)

Divide 3 into 5:

| 1 | (quotient)

3 | 5 |  

- | 3 |  

| 2 | (remainder)

5 is not divisible by 3:

3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 or 3)

No primes less than 5 divide into it. Therefore 5 is prime:

3240 = 2×2×2×3×3×3×3×5

There are 3 copies of 2, 4 copies of 3 and 1 copy of 5 in the product:

Answer:  3240 = 2^3×3^4×5