Solved on Nov 15, 2023

Find the prime factor tree of 330 and use it to calculate the highest common factor (HCF) of 308 and 330.

STEP 1

Assumptions1. The numbers are308 and330. . We need to find the highest common factor (HCF) of these numbers.
3. We will use prime factor trees to find the prime factors of these numbers.

STEP 2

Let's first draw the prime factor tree for330. We start by finding two factors of330. A simple choice is10 and33.
$330 =10 \times33$

STEP 3

Now, we break down each of these factors into their prime factors. $10 =2 \times5$ $33 =3 \times11$

STEP 4

So, the prime factor tree for330 is $330 =2 \times \times3 \times11$

STEP 5

Now, let's draw the prime factor tree for308. We start by finding two factors of308. A simple choice is2 and154.
$308 =2 \times154$

STEP 6

Now, we break down154 into its prime factors. $154 =2 \times77$

STEP 7

Finally, we break down77 into its prime factors.
$77 =7 \times11$

STEP 8

So, the prime factor tree for308 is $308 =2 \times2 \times7 \times11$

STEP 9

The highest common factor (HCF) is found by multiplying the common prime factors.The common prime factors of330 and308 are2 and11.

STEP 10

So, the HCF of330 and308 is $HCF =2 \times$

STEP 11

Calculate the HCF.
$HCF = \times11 =22$ The highest common factor (HCF) of308 and330 is22.

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Find the prime factor tree of 330 and use it to calculate the highest common factor (HCF) of 308 and 330.

STEP 1

Assumptions1. The numbers are308 and330. . We need to find the highest common factor (HCF) of these numbers.
3. We will use prime factor trees to find the prime factors of these numbers.

STEP 2

Let's first draw the prime factor tree for330. We start by finding two factors of330. A simple choice is10 and33.
$330 =10 \times33$

STEP 3

Now, we break down each of these factors into their prime factors. $10 =2 \times5$ $33 =3 \times11$

STEP 4

So, the prime factor tree for330 is $330 =2 \times \times3 \times11$

STEP 5

Now, let's draw the prime factor tree for308. We start by finding two factors of308. A simple choice is2 and154.
$308 =2 \times154$

STEP 6

Now, we break down154 into its prime factors. $154 =2 \times77$

STEP 7

Finally, we break down77 into its prime factors.
$77 =7 \times11$

STEP 8

So, the prime factor tree for308 is $308 =2 \times2 \times7 \times11$

STEP 9

The highest common factor (HCF) is found by multiplying the common prime factors.The common prime factors of330 and308 are2 and11.

STEP 10

So, the HCF of330 and308 is $HCF =2 \times$

STEP 11

Calculate the HCF.
$HCF = \times11 =22$ The highest common factor (HCF) of308 and330 is22.

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Find the prime factor tree of 330 and use it to calculate the highest common factor (HCF) of 308 and 330.

STEP 1

Assumptions1. The numbers are308 and330. . We need to find the highest common factor (HCF) of these numbers.3. We will use prime factor trees to find the prime factors of these numbers.

STEP 2

Let's first draw the prime factor tree for330. We start by finding two factors of330. A simple choice is10 and33.330=10×33330 =10 \times33330=10×33

STEP 3

Now, we break down each of these factors into their prime factors.10=2×510 =2 \times510=2×533=3×1133 =3 \times1133=3×11

STEP 4

So, the prime factor tree for330 is330=2××3×11330 =2 \times \times3 \times11330=2××3×11

STEP 5

Now, let's draw the prime factor tree for308. We start by finding two factors of308. A simple choice is2 and154.308=2×154308 =2 \times154308=2×154

STEP 6

Now, we break down154 into its prime factors.154=2×77154 =2 \times77154=2×77

STEP 7

Finally, we break down77 into its prime factors.77=7×1177 =7 \times1177=7×11

STEP 8

So, the prime factor tree for308 is308=2×2×7×11308 =2 \times2 \times7 \times11308=2×2×7×11

STEP 9

The highest common factor (HCF) is found by multiplying the common prime factors.The common prime factors of330 and308 are2 and11.

STEP 10

So, the HCF of330 and308 isHCF=2×HCF =2 \timesHCF=2×

STEP 11

Calculate the HCF.HCF=×11=22HCF = \times11 =22HCF=×11=22The highest common factor (HCF) of308 and330 is22.

Start learning now

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

Assumptions1. The numbers are308 and330. . We need to find the highest common factor (HCF) of these numbers.
3. We will use prime factor trees to find the prime factors of these numbers.

Let's first draw the prime factor tree for330. We start by finding two factors of330. A simple choice is10 and33.
$330 =10 \times33$

Now, we break down each of these factors into their prime factors. $10 =2 \times5$ $33 =3 \times11$

So, the prime factor tree for330 is $330 =2 \times \times3 \times11$

Now, let's draw the prime factor tree for308. We start by finding two factors of308. A simple choice is2 and154.
$308 =2 \times154$

Now, we break down154 into its prime factors. $154 =2 \times77$

Finally, we break down77 into its prime factors.
$77 =7 \times11$

So, the prime factor tree for308 is $308 =2 \times2 \times7 \times11$

So, the HCF of330 and308 is $HCF =2 \times$

Calculate the HCF.
$HCF = \times11 =22$ The highest common factor (HCF) of308 and330 is22.