Highest Common Factor of 706, 986, 358 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 706, 986, 358 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 986, 358 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 706, 986, 358 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 706, 986, 358 is 2.
HCF(706, 986, 358) = 2
HCF of 706, 986, 358 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 706, 986, 358 is 2.
Highest Common Factor of 706,986,358 is 2
Step 1: Since 986 > 706, we apply the division lemma to 986 and 706, to get
986 = 706 x 1 + 280
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 280 and 706, to get
706 = 280 x 2 + 146
Step 3: We consider the new divisor 280 and the new remainder 146, and apply the division lemma to get
280 = 146 x 1 + 134
We consider the new divisor 146 and the new remainder 134,and apply the division lemma to get
146 = 134 x 1 + 12
We consider the new divisor 134 and the new remainder 12,and apply the division lemma to get
134 = 12 x 11 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 986 is 2
Notice that 2 = HCF(12,2) = HCF(134,12) = HCF(146,134) = HCF(280,146) = HCF(706,280) = HCF(986,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 358 > 2, we apply the division lemma to 358 and 2, to get
358 = 2 x 179 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 358 is 2
Notice that 2 = HCF(358,2) .
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Frequently Asked Questions on HCF of 706, 986, 358 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 706, 986, 358?
Answer: HCF of 706, 986, 358 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 986, 358 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 986, 358 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.