Question
Find the highest common factor of 405 , 783, 513
286
likes1430 views
Answer to a math question Find the highest common factor of 405 , 783, 513
Ali
4.492 Answers
Solution:
1. Factorize 405:
- 405 = 3 × 135
- 135 = 3 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- Therefore, 405 = 3^4 × 5
2. Factorize 783:
- 783 = 3 × 261
- 261 = 3 × 87
- 87 = 3 × 29
- 29 is prime.
- Therefore, 783 = 3^3 × 29
3. Factorize 513:
- 513 = 3 × 171
- 171 = 3 × 57
- 57 = 3 × 19
- 19 is prime.
- Therefore, 513 = 3^3 × 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 × 135
- 135 = 3 × 45
- 45 = 3 × 15
- 15 = 3 × 5
- Therefore, 405 = 3^4 × 5
2. Factorize 783:
- 783 = 3 × 261
- 261 = 3 × 87
- 87 = 3 × 29
- 29 is prime.
- Therefore, 783 = 3^3 × 29
3. Factorize 513:
- 513 = 3 × 171
- 171 = 3 × 57
- 57 = 3 × 19
- 19 is prime.
- Therefore, 513 = 3^3 × 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:
Frequently asked questions (FAQs)
Math Question: Find the derivative of f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 9.
+
What is the Pythagorean theorem formula for finding the length of the hypotenuse in a right-angled triangle?
+
Math Question: Find the measure of angle A in triangle ABC if the angle bisector of angle A splits BC into segments of length 8 and 12.
+
New questions in Mathematics