Find the h c f 486,729, 1296
Answers
To find the HCF of the given three numbers, two methods can be used:
- Prime Factorization method
- Euclid's division algorithm
Solving through the prime factorization method:
486 = 2 x 3 x 3 x 3 x 3 x 3
729 = 3 × 3 × 3 × 3 × 3 × 3
1296 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3
Now, the bolded numbers are the prime factors that occur in all the three numbers:
3 x 3 x 3 x 3 occur in all the three numbers and the product will be the highest common factor.
3 x 3 x 3 x 3 = 81
The HCF is 81.
Solving through Euclid's division lemma:
Please refer the attachment to view the long division procedure.
In Euclid's division lemma, we find the HCF of two of the numbers by constant division until the remainder becomes 0. Then, we find the HCF of the last divisor in the first division process and the third number. The last divisor in the second process is the HCF of all the three numbers.
Knowledge Bytes:
- What is HCF?
Highest Common Factor (HCF) is the largest number that is the common and the largest factor of two or more numbers. HCF can be found out using prime factorization method as well as through Euclid's division algorithm.
Step-by-step explanation:
Answer
Step-by-step explanation:
486=2*3*3*3*3*3=2*3^5
729=27^2=(3^3)^2=3^6
1296=36*36=6^4=(2*3)^4=2^4*3^4
highest common factor in the 3 factor is
3^4
hcf is 3^4-81
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