Math  /  Numbers & Operations

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Sparx Maths 2A 2B 2 C Summary Bookwork code: 2C Calculator allowed
The prime factor tree for 693 is given below. Draw the prime factor tree for 330 and use it to work out the highest comm factor (HCF) of 330 and 693. Previous Watch video

Studdy Solution

STEP 1

1. We need to find the prime factors of 330.
2. We need to use the prime factors of 330 and 693 to find their highest common factor (HCF).
3. The prime factor tree for 693 is given as 3×3×7×11 3 \times 3 \times 7 \times 11 .

STEP 2

1. Draw the prime factor tree for 330.
2. List the prime factors of 330.
3. Identify the common prime factors of 330 and 693.
4. Calculate the highest common factor (HCF).

STEP 3

Start by dividing 330 by the smallest prime number, 2, since 330 is even.
330÷2=165 330 \div 2 = 165

STEP 4

Continue factoring 165 by the next smallest prime number, 3, since the sum of the digits of 165 is divisible by 3.
165÷3=55 165 \div 3 = 55

STEP 5

Factor 55 by the next smallest prime number, 5, since 55 ends in 5.
55÷5=11 55 \div 5 = 11

STEP 6

Finally, 11 is a prime number.

STEP 7

List the prime factors of 330:
330=2×3×5×11 330 = 2 \times 3 \times 5 \times 11

STEP 8

List the prime factors of 693, which are given as:
693=3×3×7×11 693 = 3 \times 3 \times 7 \times 11

STEP 9

Identify the common prime factors of 330 and 693:
- Common prime factors: 3 3 and 11 11

STEP 10

Calculate the highest common factor (HCF) by multiplying the common prime factors:
HCF=3×11=33 \text{HCF} = 3 \times 11 = 33
The highest common factor (HCF) of 330 and 693 is:
33\boxed{33}

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