Math / Algebra

QuestionFind the greatest common factor of $10 n^{4}$ and $7 c^{3}$ . $\square$

Studdy Solution

STEP 1

What is this asking? Find the biggest value that divides evenly into both $10n^4$ and $7c^3$ . Watch out! Don't mix up greatest common factor (GCF) with least common multiple (LCM)!

STEP 2

1. Find the prime factors.
2. Identify common factors.
3. Calculate the GCF.

STEP 3

Let's break down $10n^4$ into its prime factors!
We've got $10$ which is $2 \cdot 5$ , and $n^4$ which is $n \cdot n \cdot n \cdot n$ .
So, $10n^4 = 2 \cdot 5 \cdot n \cdot n \cdot n \cdot n$ .
See? Not so scary!

STEP 4

Now let's do the same for $7c^3$ . $7$ is already a prime number, how convenient!
And $c^3$ is just $c \cdot c \cdot c$ .
So $7c^3 = 7 \cdot c \cdot c \cdot c$ .

STEP 5

Now, let's look for what they have in common.
We're looking for factors that appear in both $10n^4$ and $7c^3$ .
Hmm, I see a whole lotta noughts in the first one, and a whole lotta c's in the second one, but none of those are shared.
The numbers $2$ , $5$ , and $7$ are all different prime numbers, so there are no common numerical factors either.

STEP 6

Since there are no common prime factors between $2 \cdot 5 \cdot n \cdot n \cdot n \cdot n$ and $7 \cdot c \cdot c \cdot c$ , the only factor they share is $1$ .
Anything multiplied by $1$ is itself, so $1$ is a common factor for everything!

STEP 7

The greatest common factor of $10n^4$ and $7c^3$ is $1$ .

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QuestionFind the greatest common factor of $10 n^{4}$ and $7 c^{3}$ . $\square$

Studdy Solution

STEP 1

What is this asking? Find the biggest value that divides evenly into both $10n^4$ and $7c^3$ . Watch out! Don't mix up greatest common factor (GCF) with least common multiple (LCM)!

STEP 2

1. Find the prime factors.
2. Identify common factors.
3. Calculate the GCF.

STEP 3

Let's break down $10n^4$ into its prime factors!
We've got $10$ which is $2 \cdot 5$ , and $n^4$ which is $n \cdot n \cdot n \cdot n$ .
So, $10n^4 = 2 \cdot 5 \cdot n \cdot n \cdot n \cdot n$ .
See? Not so scary!

STEP 4

Now let's do the same for $7c^3$ . $7$ is already a prime number, how convenient!
And $c^3$ is just $c \cdot c \cdot c$ .
So $7c^3 = 7 \cdot c \cdot c \cdot c$ .

STEP 5

STEP 6

Since there are no common prime factors between $2 \cdot 5 \cdot n \cdot n \cdot n \cdot n$ and $7 \cdot c \cdot c \cdot c$ , the only factor they share is $1$ .
Anything multiplied by $1$ is itself, so $1$ is a common factor for everything!

STEP 7

The greatest common factor of $10n^4$ and $7c^3$ is $1$ .

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QuestionFind the greatest common factor of 10n410 n^{4}10n4 and 7c37 c^{3}7c3. □\square□

Studdy Solution

STEP 1

What is this asking? Find the biggest value that divides evenly into both 10n410n^410n4 and 7c37c^37c3. Watch out! Don't mix up greatest common factor (GCF) with least common multiple (LCM)!

STEP 2

1. Find the prime factors.2. Identify common factors.3. Calculate the GCF.

STEP 3

STEP 4

Now let's do the same for 7c37c^37c3. 777 is already a prime number, how convenient!And c3c^3c3 is just c⋅c⋅cc \cdot c \cdot cc⋅c⋅c.So 7c3=7⋅c⋅c⋅c7c^3 = 7 \cdot c \cdot c \cdot c7c3=7⋅c⋅c⋅c.

STEP 5

STEP 6

STEP 7

The greatest common factor of 10n410n^410n4 and 7c37c^37c3 is 111.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the greatest common factor of $10 n^{4}$ and $7 c^{3}$ . $\square$

What is this asking? Find the biggest value that divides evenly into both $10n^4$ and $7c^3$ . Watch out! Don't mix up greatest common factor (GCF) with least common multiple (LCM)!

1. Find the prime factors.
2. Identify common factors.
3. Calculate the GCF.

Now let's do the same for $7c^3$ . $7$ is already a prime number, how convenient!
And $c^3$ is just $c \cdot c \cdot c$ .
So $7c^3 = 7 \cdot c \cdot c \cdot c$ .

The greatest common factor of $10n^4$ and $7c^3$ is $1$ .