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=10×33330 =10 \times33

STEP 3

Now, we break down each of these factors into their prime factors.10=2×510 =2 \times533=3×1133 =3 \times11

STEP 4

So, the prime factor tree for330 is330=2××3×11330 =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=2×154308 =2 \times154

STEP 6

Now, we break down154 into its prime factors.154=2×77154 =2 \times77

STEP 7

Finally, we break down77 into its prime factors.
77=7×1177 =7 \times11

STEP 8

So, the prime factor tree for308 is308=2×2×7×11308 =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 isHCF=2×HCF =2 \times

STEP 11

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

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