Highest Common Factor of 746, 682, 348 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 746, 682, 348 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 746, 682, 348 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 746, 682, 348 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 746, 682, 348 is 2.
HCF(746, 682, 348) = 2
HCF of 746, 682, 348 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 746, 682, 348 is 2.
Highest Common Factor of 746,682,348 is 2
Step 1: Since 746 > 682, we apply the division lemma to 746 and 682, to get
746 = 682 x 1 + 64
Step 2: Since the reminder 682 ≠ 0, we apply division lemma to 64 and 682, to get
682 = 64 x 10 + 42
Step 3: We consider the new divisor 64 and the new remainder 42, and apply the division lemma to get
64 = 42 x 1 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 746 and 682 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(64,42) = HCF(682,64) = HCF(746,682) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 348 > 2, we apply the division lemma to 348 and 2, to get
348 = 2 x 174 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 348 is 2
Notice that 2 = HCF(348,2) .
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Frequently Asked Questions on HCF of 746, 682, 348 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 746, 682, 348?
Answer: HCF of 746, 682, 348 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 746, 682, 348 using Euclid's Algorithm?
Answer: For arbitrary numbers 746, 682, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.