Highest Common Factor of 614, 972, 31 using Euclid's algorithm
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 614, 972, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 614, 972, 31 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 614, 972, 31 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 614, 972, 31 is 1.
HCF(614, 972, 31) = 1
HCF of 614, 972, 31 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 614, 972, 31 is 1.
Highest Common Factor of 614,972,31 is 1
Step 1: Since 972 > 614, we apply the division lemma to 972 and 614, to get
972 = 614 x 1 + 358
Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 358 and 614, to get
614 = 358 x 1 + 256
Step 3: We consider the new divisor 358 and the new remainder 256, and apply the division lemma to get
358 = 256 x 1 + 102
We consider the new divisor 256 and the new remainder 102,and apply the division lemma to get
256 = 102 x 2 + 52
We consider the new divisor 102 and the new remainder 52,and apply the division lemma to get
102 = 52 x 1 + 50
We consider the new divisor 52 and the new remainder 50,and apply the division lemma to get
52 = 50 x 1 + 2
We consider the new divisor 50 and the new remainder 2,and apply the division lemma to get
50 = 2 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 972 is 2
Notice that 2 = HCF(50,2) = HCF(52,50) = HCF(102,52) = HCF(256,102) = HCF(358,256) = HCF(614,358) = HCF(972,614) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 2, we apply the division lemma to 31 and 2, to get
31 = 2 x 15 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 31 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) .
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Frequently Asked Questions on HCF of 614, 972, 31 using Euclid's Algorithm
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 614, 972, 31?
Answer: HCF of 614, 972, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 614, 972, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 614, 972, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.