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, 9102, 3203 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 967, 9102, 3203 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, 9102, 3203 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, 9102, 3203 is 1.
HCF(967, 9102, 3203) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 967, 9102, 3203 is 1.
Step 1: Since 9102 > 967, we apply the division lemma to 9102 and 967, to get
9102 = 967 x 9 + 399
Step 2: Since the reminder 967 ≠ 0, we apply division lemma to 399 and 967, to get
967 = 399 x 2 + 169
Step 3: We consider the new divisor 399 and the new remainder 169, and apply the division lemma to get
399 = 169 x 2 + 61
We consider the new divisor 169 and the new remainder 61,and apply the division lemma to get
169 = 61 x 2 + 47
We consider the new divisor 61 and the new remainder 47,and apply the division lemma to get
61 = 47 x 1 + 14
We consider the new divisor 47 and the new remainder 14,and apply the division lemma to get
47 = 14 x 3 + 5
We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get
14 = 5 x 2 + 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 9102 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(47,14) = HCF(61,47) = HCF(169,61) = HCF(399,169) = HCF(967,399) = HCF(9102,967) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3203 > 1, we apply the division lemma to 3203 and 1, to get
3203 = 1 x 3203 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3203 is 1
Notice that 1 = HCF(3203,1) .
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, 9102, 3203?
Answer: HCF of 967, 9102, 3203 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 967, 9102, 3203 using Euclid's Algorithm?
Answer: For arbitrary numbers 967, 9102, 3203 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.