Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 649, 6765 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 649, 6765 is 11 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 649, 6765 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 649, 6765 is 11.
HCF(649, 6765) = 11
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 649, 6765 is 11.
Step 1: Since 6765 > 649, we apply the division lemma to 6765 and 649, to get
6765 = 649 x 10 + 275
Step 2: Since the reminder 649 ≠ 0, we apply division lemma to 275 and 649, to get
649 = 275 x 2 + 99
Step 3: We consider the new divisor 275 and the new remainder 99, and apply the division lemma to get
275 = 99 x 2 + 77
We consider the new divisor 99 and the new remainder 77,and apply the division lemma to get
99 = 77 x 1 + 22
We consider the new divisor 77 and the new remainder 22,and apply the division lemma to get
77 = 22 x 3 + 11
We consider the new divisor 22 and the new remainder 11,and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 649 and 6765 is 11
Notice that 11 = HCF(22,11) = HCF(77,22) = HCF(99,77) = HCF(275,99) = HCF(649,275) = HCF(6765,649) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 649, 6765?
Answer: HCF of 649, 6765 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 649, 6765 using Euclid's Algorithm?
Answer: For arbitrary numbers 649, 6765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.