Highest Common Factor of 756, 595, 686 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 756, 595, 686 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 595, 686 is 7 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 756, 595, 686 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 756, 595, 686 is 7.
HCF(756, 595, 686) = 7
HCF of 756, 595, 686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 595, 686 is 7.
Highest Common Factor of 756,595,686 is 7
Step 1: Since 756 > 595, we apply the division lemma to 756 and 595, to get
756 = 595 x 1 + 161
Step 2: Since the reminder 595 ≠ 0, we apply division lemma to 161 and 595, to get
595 = 161 x 3 + 112
Step 3: We consider the new divisor 161 and the new remainder 112, and apply the division lemma to get
161 = 112 x 1 + 49
We consider the new divisor 112 and the new remainder 49,and apply the division lemma to get
112 = 49 x 2 + 14
We consider the new divisor 49 and the new remainder 14,and apply the division lemma to get
49 = 14 x 3 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 756 and 595 is 7
Notice that 7 = HCF(14,7) = HCF(49,14) = HCF(112,49) = HCF(161,112) = HCF(595,161) = HCF(756,595) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 7, we apply the division lemma to 686 and 7, to get
686 = 7 x 98 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 686 is 7
Notice that 7 = HCF(686,7) .
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Frequently Asked Questions on HCF of 756, 595, 686 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 756, 595, 686?
Answer: HCF of 756, 595, 686 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 595, 686 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 595, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
