Find the prime factorization for the following numbers: 50, 80, 144, 95, and 125.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the prime factorizations for each number using a factor tree approach:

1) For 50:

Break down 50 into two factors.
$50 = 2 \times 25$
Break down 25 into its factors.
$25 = 5 \times 5$
Combine all prime factors.
$50 = 2 \times 5 \times 5 = 2 \times 5^2$
The prime factors of 50 are $\boxed{\text{2, 5}}$ .

2) For 80:
Break down 80 into two factors.
$80 = 8 \times 10$
Break down 8 and 10 into their factors.
$8 = 2 \times 4 = 2 \times 2 \times 2 = 2^3$ $10 = 2 \times 5$
Combine all prime factors.
$80 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5$
The prime factors of 80 are $\boxed{\text{2, 5}}$ .

3) For 144:
Break down 144 into two factors.
$144 = 12 \times 12$
Break down each 12 into its factors.
$12 = 2 \times 6 = 2 \times 2 \times 3 = 2^2 \times 3$
Combine all prime factors.
$144 = (2 \times 2 \times 3) \times (2 \times 2 \times 3) = 2^4 \times 3^2$
The prime factors of 144 are $\boxed{\text{2, 3}}$ .

4) For 95:
Break down 95 into two factors.
$95 = 5 \times 19$
Both 5 and 19 are prime numbers.
Combine all prime factors.
$95 = 5 \times 19$
The prime factors of 95 are $\boxed{\text{5, 19}}$ .

5) For 125:
Break down 125 into two factors.
$125 = 5 \times 25$
Break down 25 into its factors.
$25 = 5 \times 5$
Combine all prime factors.
$125 = 5 \times 5 \times 5 = 5^3$
The prime factors of 125 are $\boxed{\text{5}}$ .

6) For 132:
Break down 132 into two factors.
$132 = 2 \times 66$
Break down 66 into its factors.
$66 = 2 \times 33$
Break down 33 into its factors.
$33 = 3 \times 11$
Combine all prime factors.
$132 = 2 \times 2 \times 3 \times 11 = 2^2 \times 3 \times 11$
The prime factors of 132 are $\boxed{\text{2, 3, 11}}$ .

7) For 72:
Break down 72 into two factors.
$72 = 8 \times 9$
Break down 8 and 9 into their factors.
$8 = 2 \times 4 = 2 \times 2 \times 2 = 2^3$ $9 = 3 \times 3 = 3^2$
Combine all prime factors.
$72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2$
The prime factors of 72 are $\boxed{\text{2, 3}}$ .

8) For 30:
Break down 30 into two factors.
$30 = 3 \times 10$
Break down 10 into its factors.
$10 = 2 \times 5$
Combine all prime factors.
$30 = 2 \times 3 \times 5$
The prime factors of 30 are $\boxed{\text{2, 3, 5}}$ .

9) For 63:
Break down 63 into two factors.
$63 = 7 \times 9$
Break down 9 into its factors.
$9 = 3 \times 3 = 3^2$
Combine all prime factors.
$63 = 3 \times 3 \times 7 = 3^2 \times 7$
The prime factors of 63 are $\boxed{\text{3, 7}}$ .

10) For 54:
Break down 54 into two factors.
$54 = 6 \times 9$
Break down 6 and 9 into their factors.
$6 = 2 \times 3$ $9 = 3 \times 3 = 3^2$
Combine all prime factors.
$54 = 2 \times 3 \times 3 \times 3 = 2 \times 3^3$
The prime factors of 54 are $\boxed{\text{2, 3}}$ .

Find the prime factorization for the following numbers: 50, 80, 144, 95, and 125.

Step-by-step solution

Break down 50 into two factors.

Break down 25 into its factors.

Combine all prime factors.

Break down 80 into two factors.

Break down 8 and 10 into their factors.

Combine all prime factors.

Break down 144 into two factors.

Break down each 12 into its factors.

Combine all prime factors.

Break down 95 into two factors.

Both 5 and 19 are prime numbers.

Combine all prime factors.

Break down 125 into two factors.

Break down 25 into its factors.

Combine all prime factors.

Break down 132 into two factors.

Break down 66 into its factors.

Break down 33 into its factors.

Combine all prime factors.

Break down 72 into two factors.

Break down 8 and 9 into their factors.

Combine all prime factors.

Break down 30 into two factors.

Break down 10 into its factors.

Combine all prime factors.

Break down 63 into two factors.

Break down 9 into its factors.

Combine all prime factors.

Break down 54 into two factors.

Break down 6 and 9 into their factors.

Combine all prime factors.

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