Highest Common Factor of 821, 680, 974 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 821, 680, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 680, 974 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 821, 680, 974 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 821, 680, 974 is 1.
HCF(821, 680, 974) = 1
HCF of 821, 680, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 680, 974 is 1.
Highest Common Factor of 821,680,974 is 1
Step 1: Since 821 > 680, we apply the division lemma to 821 and 680, to get
821 = 680 x 1 + 141
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 141 and 680, to get
680 = 141 x 4 + 116
Step 3: We consider the new divisor 141 and the new remainder 116, and apply the division lemma to get
141 = 116 x 1 + 25
We consider the new divisor 116 and the new remainder 25,and apply the division lemma to get
116 = 25 x 4 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 821 and 680 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(116,25) = HCF(141,116) = HCF(680,141) = HCF(821,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 1, we apply the division lemma to 974 and 1, to get
974 = 1 x 974 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 974 is 1
Notice that 1 = HCF(974,1) .
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Frequently Asked Questions on HCF of 821, 680, 974 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 821, 680, 974?
Answer: HCF of 821, 680, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 680, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 680, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.