Highest Common Factor of 344, 646, 974 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 344, 646, 974 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 344, 646, 974 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 344, 646, 974 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 344, 646, 974 is 2.
HCF(344, 646, 974) = 2
HCF of 344, 646, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 344, 646, 974 is 2.
Highest Common Factor of 344,646,974 is 2
Step 1: Since 646 > 344, we apply the division lemma to 646 and 344, to get
646 = 344 x 1 + 302
Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 302 and 344, to get
344 = 302 x 1 + 42
Step 3: We consider the new divisor 302 and the new remainder 42, and apply the division lemma to get
302 = 42 x 7 + 8
We consider the new divisor 42 and the new remainder 8,and apply the division lemma to get
42 = 8 x 5 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 344 and 646 is 2
Notice that 2 = HCF(8,2) = HCF(42,8) = HCF(302,42) = HCF(344,302) = HCF(646,344) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 2, we apply the division lemma to 974 and 2, to get
974 = 2 x 487 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 974 is 2
Notice that 2 = HCF(974,2) .
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Frequently Asked Questions on HCF of 344, 646, 974 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 344, 646, 974?
Answer: HCF of 344, 646, 974 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 344, 646, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 344, 646, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.