Highest Common Factor of 658, 756, 343 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 658, 756, 343 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 756, 343 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 658, 756, 343 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 658, 756, 343 is 7.
HCF(658, 756, 343) = 7
HCF of 658, 756, 343 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 756, 343 is 7.
Highest Common Factor of 658,756,343 is 7
Step 1: Since 756 > 658, we apply the division lemma to 756 and 658, to get
756 = 658 x 1 + 98
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 98 and 658, to get
658 = 98 x 6 + 70
Step 3: We consider the new divisor 98 and the new remainder 70, and apply the division lemma to get
98 = 70 x 1 + 28
We consider the new divisor 70 and the new remainder 28,and apply the division lemma to get
70 = 28 x 2 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 658 and 756 is 14
Notice that 14 = HCF(28,14) = HCF(70,28) = HCF(98,70) = HCF(658,98) = HCF(756,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 343 > 14, we apply the division lemma to 343 and 14, to get
343 = 14 x 24 + 7
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 7 and 14, 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 14 and 343 is 7
Notice that 7 = HCF(14,7) = HCF(343,14) .
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Frequently Asked Questions on HCF of 658, 756, 343 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 658, 756, 343?
Answer: HCF of 658, 756, 343 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 756, 343 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 756, 343 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.