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 987, 710, 830 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 710, 830 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 987, 710, 830 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 987, 710, 830 is 1.
HCF(987, 710, 830) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 710, 830 is 1.
Step 1: Since 987 > 710, we apply the division lemma to 987 and 710, to get
987 = 710 x 1 + 277
Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 277 and 710, to get
710 = 277 x 2 + 156
Step 3: We consider the new divisor 277 and the new remainder 156, and apply the division lemma to get
277 = 156 x 1 + 121
We consider the new divisor 156 and the new remainder 121,and apply the division lemma to get
156 = 121 x 1 + 35
We consider the new divisor 121 and the new remainder 35,and apply the division lemma to get
121 = 35 x 3 + 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 987 and 710 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(35,16) = HCF(121,35) = HCF(156,121) = HCF(277,156) = HCF(710,277) = HCF(987,710) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 830 > 1, we apply the division lemma to 830 and 1, to get
830 = 1 x 830 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 830 is 1
Notice that 1 = HCF(830,1) .
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 987, 710, 830?
Answer: HCF of 987, 710, 830 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 710, 830 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 710, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.