Highest Common Factor of 706, 980, 659 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, 980, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 706, 980, 659 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 706, 980, 659 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, 980, 659 is 1.
HCF(706, 980, 659) = 1
HCF of 706, 980, 659 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, 980, 659 is 1.
Highest Common Factor of 706,980,659 is 1
Step 1: Since 980 > 706, we apply the division lemma to 980 and 706, to get
980 = 706 x 1 + 274
Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 274 and 706, to get
706 = 274 x 2 + 158
Step 3: We consider the new divisor 274 and the new remainder 158, and apply the division lemma to get
274 = 158 x 1 + 116
We consider the new divisor 158 and the new remainder 116,and apply the division lemma to get
158 = 116 x 1 + 42
We consider the new divisor 116 and the new remainder 42,and apply the division lemma to get
116 = 42 x 2 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 706 and 980 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(116,42) = HCF(158,116) = HCF(274,158) = HCF(706,274) = HCF(980,706) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 659 > 2, we apply the division lemma to 659 and 2, to get
659 = 2 x 329 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 659 is 1
Notice that 1 = HCF(2,1) = HCF(659,2) .
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Frequently Asked Questions on HCF of 706, 980, 659 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, 980, 659?
Answer: HCF of 706, 980, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 706, 980, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 706, 980, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.