Highest Common Factor of 874, 542, 738 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 874, 542, 738 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 542, 738 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 874, 542, 738 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 874, 542, 738 is 2.
HCF(874, 542, 738) = 2
HCF of 874, 542, 738 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 542, 738 is 2.
Highest Common Factor of 874,542,738 is 2
Step 1: Since 874 > 542, we apply the division lemma to 874 and 542, to get
874 = 542 x 1 + 332
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 332 and 542, to get
542 = 332 x 1 + 210
Step 3: We consider the new divisor 332 and the new remainder 210, and apply the division lemma to get
332 = 210 x 1 + 122
We consider the new divisor 210 and the new remainder 122,and apply the division lemma to get
210 = 122 x 1 + 88
We consider the new divisor 122 and the new remainder 88,and apply the division lemma to get
122 = 88 x 1 + 34
We consider the new divisor 88 and the new remainder 34,and apply the division lemma to get
88 = 34 x 2 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 874 and 542 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(88,34) = HCF(122,88) = HCF(210,122) = HCF(332,210) = HCF(542,332) = HCF(874,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 738 > 2, we apply the division lemma to 738 and 2, to get
738 = 2 x 369 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 738 is 2
Notice that 2 = HCF(738,2) .
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Frequently Asked Questions on HCF of 874, 542, 738 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 874, 542, 738?
Answer: HCF of 874, 542, 738 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 542, 738 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 542, 738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.