Solved on Nov 08, 2023

Find the prime factorization of 25 and 42.

STEP 1

Assumptions1. We are asked to express the numbers25 and42 as a product of their prime factors. . Prime factors of a number are the prime numbers that divide that number exactly.

STEP 2

We start with the number25. To find the prime factors, we start by dividing the number by the smallest prime number, which is2. If it's not divisible by2, we move to the next prime number, which is, and so on.

STEP 3

Since25 is not divisible by2, we try the next prime number, which is3. Again,25 is not divisible by3. The next prime number is5, and25 is divisible by5.
$25 =5 \times5$

STEP 4

So, the prime factorization of25 is $\times$ or $^2$ .

STEP 5

Next, we find the prime factors of42. We start by dividing42 by the smallest prime number, which is2.42 is divisible by2.
$42 =2 \times21$

STEP 6

Next, we find the prime factors of21.21 is not divisible by2, but it is divisible by the next prime number, which is3.
$21 =3 \times$

STEP 7

So, the prime factorization of42 is $2 \times3 \times7$ .
In conclusion, the prime factorization of25 is $5^2$ and the prime factorization of42 is $2 \times3 \times7$ .

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Find the prime factorization of 25 and 42.

STEP 1

Assumptions1. We are asked to express the numbers25 and42 as a product of their prime factors. . Prime factors of a number are the prime numbers that divide that number exactly.

STEP 2

We start with the number25. To find the prime factors, we start by dividing the number by the smallest prime number, which is2. If it's not divisible by2, we move to the next prime number, which is, and so on.

STEP 3

Since25 is not divisible by2, we try the next prime number, which is3. Again,25 is not divisible by3. The next prime number is5, and25 is divisible by5.
$25 =5 \times5$

STEP 4

So, the prime factorization of25 is $\times$ or $^2$ .

STEP 5

Next, we find the prime factors of42. We start by dividing42 by the smallest prime number, which is2.42 is divisible by2.
$42 =2 \times21$

STEP 6

Next, we find the prime factors of21.21 is not divisible by2, but it is divisible by the next prime number, which is3.
$21 =3 \times$

STEP 7

So, the prime factorization of42 is $2 \times3 \times7$ .
In conclusion, the prime factorization of25 is $5^2$ and the prime factorization of42 is $2 \times3 \times7$ .

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Find the prime factorization of 25 and 42.

STEP 1

Assumptions1. We are asked to express the numbers25 and42 as a product of their prime factors. . Prime factors of a number are the prime numbers that divide that number exactly.

STEP 2

We start with the number25. To find the prime factors, we start by dividing the number by the smallest prime number, which is2. If it's not divisible by2, we move to the next prime number, which is, and so on.

STEP 3

Since25 is not divisible by2, we try the next prime number, which is3. Again,25 is not divisible by3. The next prime number is5, and25 is divisible by5.25=5×525 =5 \times525=5×5

STEP 4

So, the prime factorization of25 is × \times× or 2^22.

STEP 5

Next, we find the prime factors of42. We start by dividing42 by the smallest prime number, which is2.42 is divisible by2.42=2×2142 =2 \times2142=2×21

STEP 6

Next, we find the prime factors of21.21 is not divisible by2, but it is divisible by the next prime number, which is3.21=3×21 =3 \times21=3×

STEP 7

So, the prime factorization of42 is 2×3×72 \times3 \times72×3×7.In conclusion, the prime factorization of25 is 525^252 and the prime factorization of42 is 2×3×72 \times3 \times72×3×7.

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Since25 is not divisible by2, we try the next prime number, which is3. Again,25 is not divisible by3. The next prime number is5, and25 is divisible by5.
$25 =5 \times5$

So, the prime factorization of25 is $\times$ or $^2$ .

Next, we find the prime factors of42. We start by dividing42 by the smallest prime number, which is2.42 is divisible by2.
$42 =2 \times21$

Next, we find the prime factors of21.21 is not divisible by2, but it is divisible by the next prime number, which is3.
$21 =3 \times$

So, the prime factorization of42 is $2 \times3 \times7$ .
In conclusion, the prime factorization of25 is $5^2$ and the prime factorization of42 is $2 \times3 \times7$ .