Highest Common Factor of 974, 706, 878 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 974, 706, 878 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 706, 878 is 2 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 974, 706, 878 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 974, 706, 878 is 2.
HCF(974, 706, 878) = 2
HCF of 974, 706, 878 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 706, 878 is 2.
Highest Common Factor of 974,706,878 is 2
Step 1: Since 974 > 706, we apply the division lemma to 974 and 706, to get
974 = 706 x 1 + 268
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 268 and 706, to get
706 = 268 x 2 + 170
Step 3: We consider the new divisor 268 and the new remainder 170, and apply the division lemma to get
268 = 170 x 1 + 98
We consider the new divisor 170 and the new remainder 98,and apply the division lemma to get
170 = 98 x 1 + 72
We consider the new divisor 98 and the new remainder 72,and apply the division lemma to get
98 = 72 x 1 + 26
We consider the new divisor 72 and the new remainder 26,and apply the division lemma to get
72 = 26 x 2 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 706 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(72,26) = HCF(98,72) = HCF(170,98) = HCF(268,170) = HCF(706,268) = HCF(974,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 878 > 2, we apply the division lemma to 878 and 2, to get
878 = 2 x 439 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 878 is 2
Notice that 2 = HCF(878,2) .
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Frequently Asked Questions on HCF of 974, 706, 878 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 974, 706, 878?
Answer: HCF of 974, 706, 878 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 706, 878 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 706, 878 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.