Highest Common Factor of 714, 496, 874 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 714, 496, 874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 496, 874 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 714, 496, 874 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 714, 496, 874 is 2.
HCF(714, 496, 874) = 2
HCF of 714, 496, 874 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 496, 874 is 2.
Highest Common Factor of 714,496,874 is 2
Step 1: Since 714 > 496, we apply the division lemma to 714 and 496, to get
714 = 496 x 1 + 218
Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 218 and 496, to get
496 = 218 x 2 + 60
Step 3: We consider the new divisor 218 and the new remainder 60, and apply the division lemma to get
218 = 60 x 3 + 38
We consider the new divisor 60 and the new remainder 38,and apply the division lemma to get
60 = 38 x 1 + 22
We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 714 and 496 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(60,38) = HCF(218,60) = HCF(496,218) = HCF(714,496) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 874 > 2, we apply the division lemma to 874 and 2, to get
874 = 2 x 437 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 874 is 2
Notice that 2 = HCF(874,2) .
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Frequently Asked Questions on HCF of 714, 496, 874 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 714, 496, 874?
Answer: HCF of 714, 496, 874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 496, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 496, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.