- Home/
- CTET & State TET (Earlier - TEACHING)/
- General /
- Article
Use Euclid’s division algorithm to find the HCF of 867 and 255
By BYJU'S Exam Prep
Updated on: September 25th, 2023
According to Euclid’s Division Algorithm, if there are any two integers, a and b, then q and r must also exist in order to satisfy the given condition a = bq + r where 0 ≤ r < b.
Given numbers: 867 and 255
To find: HCF of 867 and 255 using Euclid’s Division Algorithm.
867 will be divided by 255 because 867 is greater than 255.
867 = 255 × 3 + 102
Now divide 255 by 102,
255 = 102 × 2 + 51
Now, 102 will be divided by 51
102 = 51 × 2 + 0
Therefore, the HCF of 867 and 255 using Euclid’s Division Algorithm is 51 because the remainder is zero.
Table of content
HCF of 867 and 255 using Euclid’s Division Algorithm
As discussed above, the HCF of 867 and 255 using Euclid’s Division Algorithm is 51. The Euclidean algorithm, prime factorization, and long division are the three most frequently used methods for determining the HCF of 867 and 255.
- The largest number that divides 867 and 255 exactly and without a remainder is called the HCF of 867 and 255.
- 1, 3, 17, 51, 289, 867 and 1, 3, 5, 15, 17, 51, 85, 255 are the factors of 867 and 255, respectively.
- The largest positive integer that divides two or more positive integers without leaving a remainder is known as the highest common factor, or HCF, and according to the rules of mathematics, this is usually the largest positive integer.
Summary:
Use Euclid’s Division Algorithm to find the HCF of 867 and 255.
51 is the HCF of 867 and 255 using Euclid’s Division Algorithm. Euclid’s Division Algorithm is one of the frequently used methods for finding the Highest Common Factor of any given numbers.
Related Questions:
- Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = the product of the two numbers 26 and 91
- If a = 23×3, b = 2×3× 5, c = 3n×5 and LCM (a, b, c) = 23×32×5, then n = ?
- If the HCF of 408 and 1032 is expressible in the form 1032 m − 408 × 5, find m
- Express the HCF of 468 and 222 as 468x + 222y where x and y are integers
- If a number ‘x’ is divisible by another number ‘y’, then ‘x’ is also divisible by all the prime factors of ‘y’
- How Many Terms of the AP 9, 17, 25, . . . must be taken to Give a Sum of 636?
- Verify that -(-x) = x for (i) x = 11/15 (ii) x = -13/17
