Highest Common Factor of 922, 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 922, 674 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 922, 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 922, 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 922, 674 is 2.
HCF(922, 674) = 2
HCF of 922, 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 922, 674 is 2.
Highest Common Factor of 922,674 is 2
Step 1: Since 922 > 674, we apply the division lemma to 922 and 674, to get
922 = 674 x 1 + 248
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 248 and 674, to get
674 = 248 x 2 + 178
Step 3: We consider the new divisor 248 and the new remainder 178, and apply the division lemma to get
248 = 178 x 1 + 70
We consider the new divisor 178 and the new remainder 70,and apply the division lemma to get
178 = 70 x 2 + 38
We consider the new divisor 70 and the new remainder 38,and apply the division lemma to get
70 = 38 x 1 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 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 922 and 674 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(70,38) = HCF(178,70) = HCF(248,178) = HCF(674,248) = HCF(922,674) .
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Frequently Asked Questions on HCF of 922, 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 922, 674?
Answer: HCF of 922, 674 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 922, 674 using Euclid's Algorithm?
Answer: For arbitrary numbers 922, 674 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.