Question
Find the highest common factor of 405 , 783, 513
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Answer to a math question Find the highest common factor of 405 , 783, 513
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4.492 Answers
Solution:
1. Factorize 405:
- 405 = 3 Γ 135
- 135 = 3 Γ 45
- 45 = 3 Γ 15
- 15 = 3 Γ 5
- Therefore, 405 = 3^4 Γ 5
2. Factorize 783:
- 783 = 3 Γ 261
- 261 = 3 Γ 87
- 87 = 3 Γ 29
- 29 is prime.
- Therefore, 783 = 3^3 Γ 29
3. Factorize 513:
- 513 = 3 Γ 171
- 171 = 3 Γ 57
- 57 = 3 Γ 19
- 19 is prime.
- Therefore, 513 = 3^3 Γ 19
4. Find the common prime factors:
- The common prime factor among 405, 783, and 513 is 3.
5. Identify the lowest power of the common factor:
- The lowest power of 3 common to all factorizations is 3^3.
6. The highest common factor (HCF) is therefore:
3^3 = 27
1. Factorize 405:
- 405 = 3 Γ 135
- 135 = 3 Γ 45
- 45 = 3 Γ 15
- 15 = 3 Γ 5
- Therefore, 405 = 3^4 Γ 5
2. Factorize 783:
- 783 = 3 Γ 261
- 261 = 3 Γ 87
- 87 = 3 Γ 29
- 29 is prime.
- Therefore, 783 = 3^3 Γ 29
3. Factorize 513:
- 513 = 3 Γ 171
- 171 = 3 Γ 57
- 57 = 3 Γ 19
- 19 is prime.
- Therefore, 513 = 3^3 Γ 19
4. Find the common prime factors:
- The common prime factor among 405, 783, and 513 is 3.
5. Identify the lowest power of the common factor:
- The lowest power of 3 common to all factorizations is 3^3.
6. The highest common factor (HCF) is therefore:
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