Highest Common Factor of 659, 746, 139 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 659, 746, 139 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 659, 746, 139 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 659, 746, 139 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 659, 746, 139 is 1.
HCF(659, 746, 139) = 1
HCF of 659, 746, 139 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 659, 746, 139 is 1.
Highest Common Factor of 659,746,139 is 1
Step 1: Since 746 > 659, we apply the division lemma to 746 and 659, to get
746 = 659 x 1 + 87
Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 87 and 659, to get
659 = 87 x 7 + 50
Step 3: We consider the new divisor 87 and the new remainder 50, and apply the division lemma to get
87 = 50 x 1 + 37
We consider the new divisor 50 and the new remainder 37,and apply the division lemma to get
50 = 37 x 1 + 13
We consider the new divisor 37 and the new remainder 13,and apply the division lemma to get
37 = 13 x 2 + 11
We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get
13 = 11 x 1 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 659 and 746 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(37,13) = HCF(50,37) = HCF(87,50) = HCF(659,87) = HCF(746,659) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 139 > 1, we apply the division lemma to 139 and 1, to get
139 = 1 x 139 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 139 is 1
Notice that 1 = HCF(139,1) .
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Frequently Asked Questions on HCF of 659, 746, 139 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 659, 746, 139?
Answer: HCF of 659, 746, 139 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 659, 746, 139 using Euclid's Algorithm?
Answer: For arbitrary numbers 659, 746, 139 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.