Highest Common Factor of 828, 674 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 828, 674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 674 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 828, 674 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 828, 674 is 2.
HCF(828, 674) = 2
HCF of 828, 674 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 674 is 2.
Highest Common Factor of 828,674 is 2
Step 1: Since 828 > 674, we apply the division lemma to 828 and 674, to get
828 = 674 x 1 + 154
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 154 and 674, to get
674 = 154 x 4 + 58
Step 3: We consider the new divisor 154 and the new remainder 58, and apply the division lemma to get
154 = 58 x 2 + 38
We consider the new divisor 58 and the new remainder 38,and apply the division lemma to get
58 = 38 x 1 + 20
We consider the new divisor 38 and the new remainder 20,and apply the division lemma to get
38 = 20 x 1 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 828 and 674 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(38,20) = HCF(58,38) = HCF(154,58) = HCF(674,154) = HCF(828,674) .
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Frequently Asked Questions on HCF of 828, 674 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 828, 674?
Answer: HCF of 828, 674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.