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 967, 9868, 2037 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 967, 9868, 2037 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 967, 9868, 2037 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 967, 9868, 2037 is 1.
HCF(967, 9868, 2037) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 967, 9868, 2037 is 1.
Step 1: Since 9868 > 967, we apply the division lemma to 9868 and 967, to get
9868 = 967 x 10 + 198
Step 2: Since the reminder 967 ≠ 0, we apply division lemma to 198 and 967, to get
967 = 198 x 4 + 175
Step 3: We consider the new divisor 198 and the new remainder 175, and apply the division lemma to get
198 = 175 x 1 + 23
We consider the new divisor 175 and the new remainder 23,and apply the division lemma to get
175 = 23 x 7 + 14
We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get
23 = 14 x 1 + 9
We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get
14 = 9 x 1 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 9868 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(175,23) = HCF(198,175) = HCF(967,198) = HCF(9868,967) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2037 > 1, we apply the division lemma to 2037 and 1, to get
2037 = 1 x 2037 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2037 is 1
Notice that 1 = HCF(2037,1) .
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 967, 9868, 2037?
Answer: HCF of 967, 9868, 2037 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 967, 9868, 2037 using Euclid's Algorithm?
Answer: For arbitrary numbers 967, 9868, 2037 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.