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 632, 868, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 632, 868, 617 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 632, 868, 617 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 632, 868, 617 is 1.
HCF(632, 868, 617) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 632, 868, 617 is 1.
Step 1: Since 868 > 632, we apply the division lemma to 868 and 632, to get
868 = 632 x 1 + 236
Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 236 and 632, to get
632 = 236 x 2 + 160
Step 3: We consider the new divisor 236 and the new remainder 160, and apply the division lemma to get
236 = 160 x 1 + 76
We consider the new divisor 160 and the new remainder 76,and apply the division lemma to get
160 = 76 x 2 + 8
We consider the new divisor 76 and the new remainder 8,and apply the division lemma to get
76 = 8 x 9 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 632 and 868 is 4
Notice that 4 = HCF(8,4) = HCF(76,8) = HCF(160,76) = HCF(236,160) = HCF(632,236) = HCF(868,632) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 617 > 4, we apply the division lemma to 617 and 4, to get
617 = 4 x 154 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 617 is 1
Notice that 1 = HCF(4,1) = HCF(617,4) .
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 632, 868, 617?
Answer: HCF of 632, 868, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 632, 868, 617 using Euclid's Algorithm?
Answer: For arbitrary numbers 632, 868, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.