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 857, 497, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 497, 649 is 1 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 857, 497, 649 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 857, 497, 649 is 1.
HCF(857, 497, 649) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 497, 649 is 1.
Step 1: Since 857 > 497, we apply the division lemma to 857 and 497, to get
857 = 497 x 1 + 360
Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 360 and 497, to get
497 = 360 x 1 + 137
Step 3: We consider the new divisor 360 and the new remainder 137, and apply the division lemma to get
360 = 137 x 2 + 86
We consider the new divisor 137 and the new remainder 86,and apply the division lemma to get
137 = 86 x 1 + 51
We consider the new divisor 86 and the new remainder 51,and apply the division lemma to get
86 = 51 x 1 + 35
We consider the new divisor 51 and the new remainder 35,and apply the division lemma to get
51 = 35 x 1 + 16
We consider the new divisor 35 and the new remainder 16,and apply the division lemma to get
35 = 16 x 2 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 497 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(35,16) = HCF(51,35) = HCF(86,51) = HCF(137,86) = HCF(360,137) = HCF(497,360) = HCF(857,497) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 649 > 1, we apply the division lemma to 649 and 1, to get
649 = 1 x 649 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 649 is 1
Notice that 1 = HCF(649,1) .
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 857, 497, 649?
Answer: HCF of 857, 497, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 497, 649 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 497, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.