Highest Common Factor of 784, 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 784, 874 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 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 784, 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 784, 874 is 2.
HCF(784, 874) = 2
HCF of 784, 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 784, 874 is 2.
Highest Common Factor of 784,874 is 2
Step 1: Since 874 > 784, we apply the division lemma to 874 and 784, to get
874 = 784 x 1 + 90
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 90 and 784, to get
784 = 90 x 8 + 64
Step 3: We consider the new divisor 90 and the new remainder 64, and apply the division lemma to get
90 = 64 x 1 + 26
We consider the new divisor 64 and the new remainder 26,and apply the division lemma to get
64 = 26 x 2 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 784 and 874 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(64,26) = HCF(90,64) = HCF(784,90) = HCF(874,784) .
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Frequently Asked Questions on HCF of 784, 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 784, 874?
Answer: HCF of 784, 874 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 874 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.