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 684, 969, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 969, 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 684, 969, 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 684, 969, 617 is 1.
HCF(684, 969, 617) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 969, 617 is 1.
Step 1: Since 969 > 684, we apply the division lemma to 969 and 684, to get
969 = 684 x 1 + 285
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 285 and 684, to get
684 = 285 x 2 + 114
Step 3: We consider the new divisor 285 and the new remainder 114, and apply the division lemma to get
285 = 114 x 2 + 57
We consider the new divisor 114 and the new remainder 57, and apply the division lemma to get
114 = 57 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 57, the HCF of 684 and 969 is 57
Notice that 57 = HCF(114,57) = HCF(285,114) = HCF(684,285) = HCF(969,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 617 > 57, we apply the division lemma to 617 and 57, to get
617 = 57 x 10 + 47
Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 47 and 57, to get
57 = 47 x 1 + 10
Step 3: We consider the new divisor 47 and the new remainder 10, and apply the division lemma to get
47 = 10 x 4 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 57 and 617 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(47,10) = HCF(57,47) = HCF(617,57) .
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 684, 969, 617?
Answer: HCF of 684, 969, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 969, 617 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 969, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.