Highest Common Factor of 660, 914, 726 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 660, 914, 726 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 914, 726 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 660, 914, 726 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 660, 914, 726 is 2.
HCF(660, 914, 726) = 2
HCF of 660, 914, 726 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 914, 726 is 2.
Highest Common Factor of 660,914,726 is 2
Step 1: Since 914 > 660, we apply the division lemma to 914 and 660, to get
914 = 660 x 1 + 254
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 254 and 660, to get
660 = 254 x 2 + 152
Step 3: We consider the new divisor 254 and the new remainder 152, and apply the division lemma to get
254 = 152 x 1 + 102
We consider the new divisor 152 and the new remainder 102,and apply the division lemma to get
152 = 102 x 1 + 50
We consider the new divisor 102 and the new remainder 50,and apply the division lemma to get
102 = 50 x 2 + 2
We consider the new divisor 50 and the new remainder 2,and apply the division lemma to get
50 = 2 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 660 and 914 is 2
Notice that 2 = HCF(50,2) = HCF(102,50) = HCF(152,102) = HCF(254,152) = HCF(660,254) = HCF(914,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 726 > 2, we apply the division lemma to 726 and 2, to get
726 = 2 x 363 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 726 is 2
Notice that 2 = HCF(726,2) .
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Frequently Asked Questions on HCF of 660, 914, 726 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 660, 914, 726?
Answer: HCF of 660, 914, 726 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 914, 726 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 914, 726 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.