Highest Common Factor of 751, 684 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 751, 684 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 751, 684 is 1 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 751, 684 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 751, 684 is 1.
HCF(751, 684) = 1
HCF of 751, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 751, 684 is 1.
Highest Common Factor of 751,684 is 1
Step 1: Since 751 > 684, we apply the division lemma to 751 and 684, to get
751 = 684 x 1 + 67
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 67 and 684, to get
684 = 67 x 10 + 14
Step 3: We consider the new divisor 67 and the new remainder 14, and apply the division lemma to get
67 = 14 x 4 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 751 and 684 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(67,14) = HCF(684,67) = HCF(751,684) .
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Frequently Asked Questions on HCF of 751, 684 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 751, 684?
Answer: HCF of 751, 684 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 751, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 751, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.