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 689, 977, 836 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 689, 977, 836 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 689, 977, 836 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 689, 977, 836 is 1.
HCF(689, 977, 836) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 689, 977, 836 is 1.
Step 1: Since 977 > 689, we apply the division lemma to 977 and 689, to get
977 = 689 x 1 + 288
Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 288 and 689, to get
689 = 288 x 2 + 113
Step 3: We consider the new divisor 288 and the new remainder 113, and apply the division lemma to get
288 = 113 x 2 + 62
We consider the new divisor 113 and the new remainder 62,and apply the division lemma to get
113 = 62 x 1 + 51
We consider the new divisor 62 and the new remainder 51,and apply the division lemma to get
62 = 51 x 1 + 11
We consider the new divisor 51 and the new remainder 11,and apply the division lemma to get
51 = 11 x 4 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 689 and 977 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(51,11) = HCF(62,51) = HCF(113,62) = HCF(288,113) = HCF(689,288) = HCF(977,689) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 836 > 1, we apply the division lemma to 836 and 1, to get
836 = 1 x 836 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 836 is 1
Notice that 1 = HCF(836,1) .
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 689, 977, 836?
Answer: HCF of 689, 977, 836 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 689, 977, 836 using Euclid's Algorithm?
Answer: For arbitrary numbers 689, 977, 836 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.