To solve the problem of finding the Highest Common Factor (HCF/GCD) for each pair of numbers, we will use the method of prime factorization. Here's the step-by-step solution for each pair:
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1. Find the HCF of 6 and 36
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Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 36 = 2^2 \times 3^2 \)
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Common factors: The common prime factors are \( 2 \) and \( 3 \).
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Lowest powers of common factors: \( 2^1 \times 3^1 = 6 \)
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HCF: \( 6 \)
Answer: \( \boxed{6} \)
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2. Find the HCF of 20 and 2
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Prime factorization:
- \( 20 = 2^2 \times 5 \)
- \( 2 = 2 \)
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Common factors: The common prime factor is \( 2 \).
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Lowest powers of common factors: \( 2^1 = 2 \)
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HCF: \( 2 \)
Answer: \( \boxed{2} \)
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3. Find the HCF of 2 and 38
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Prime factorization:
- \( 2 = 2 \)
- \( 38 = 2 \times 19 \)
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Common factors: The common prime factor is \( 2 \).
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Lowest powers of common factors: \( 2^1 = 2 \)
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HCF: \( 2 \)
Answer: \( \boxed{2} \)
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4. Find the HCF of 33 and 22
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Prime factorization:
- \( 33 = 3 \times 11 \)
- \( 22 = 2 \times 11 \)
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Common factors: The common prime factor is \( 11 \).
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Lowest powers of common factors: \( 11^1 = 11 \)
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HCF: \( 11 \)
Answer: \( \boxed{11} \)
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5. Find the HCF of 20 and 8
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Prime factorization:
- \( 20 = 2^2 \times 5 \)
- \( 8 = 2^3 \)
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Common factors: The common prime factor is \( 2 \).
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Lowest powers of common factors: \( 2^2 = 4 \)
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HCF: \( 4 \)
Answer: \( \boxed{4} \)
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6. Find the HCF of 39 and 3
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Prime factorization:
- \( 39 = 3 \times 13 \)
- \( 3 = 3 \)
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Common factors: The common prime factor is \( 3 \).
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Lowest powers of common factors: \( 3^1 = 3 \)
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HCF: \( 3 \)
Answer: \( \boxed{3} \)
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7. Find the HCF of 35 and 5
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Prime factorization:
- \( 35 = 5 \times 7 \)
- \( 5 = 5 \)
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Common factors: The common prime factor is \( 5 \).
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Lowest powers of common factors: \( 5^1 = 5 \)
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HCF: \( 5 \)
Answer: \( \boxed{5} \)
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8. Find the HCF of 22 and 50
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Prime factorization:
- \( 22 = 2 \times 11 \)
- \( 50 = 2 \times 5^2 \)
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Common factors: The common prime factor is \( 2 \).
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Lowest powers of common factors: \( 2^1 = 2 \)
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HCF: \( 2 \)
Answer: \( \boxed{2} \)
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9. Find the HCF of 20 and 35
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Prime factorization:
- \( 20 = 2^2 \times 5 \)
- \( 35 = 5 \times 7 \)
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Common factors: The common prime factor is \( 5 \).
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Lowest powers of common factors: \( 5^1 = 5 \)
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HCF: \( 5 \)
Answer: \( \boxed{5} \)
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10. Find the HCF of 44 and 11
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Prime factorization:
- \( 44 = 2^2 \times 11 \)
- \( 11 = 11 \)
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Common factors: The common prime factor is \( 11 \).
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Lowest powers of common factors: \( 11^1 = 11 \)
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HCF: \( 11 \)
Answer: \( \boxed{11} \)
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Final Answers:
1. \( \boxed{6} \)
2. \( \boxed{2} \)
3. \( \boxed{2} \)
4. \( \boxed{11} \)
5. \( \boxed{4} \)
6. \( \boxed{3} \)
7. \( \boxed{5} \)
8. \( \boxed{2} \)
9. \( \boxed{5} \)
10. \( \boxed{11} \)
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Summary:
The Highest Common Factors (HCFs) for the given pairs are:
\[
\boxed{6, 2, 2, 11, 4, 3, 5, 2, 5, 11}
\]
Parent Tip: Review the logic above to help your child master the concept of finding common factors worksheet.
