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 726, 509, 120, 648 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 726, 509, 120, 648 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 726, 509, 120, 648 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 726, 509, 120, 648 is 1.
HCF(726, 509, 120, 648) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 726, 509, 120, 648 is 1.
Step 1: Since 726 > 509, we apply the division lemma to 726 and 509, to get
726 = 509 x 1 + 217
Step 2: Since the reminder 509 ≠ 0, we apply division lemma to 217 and 509, to get
509 = 217 x 2 + 75
Step 3: We consider the new divisor 217 and the new remainder 75, and apply the division lemma to get
217 = 75 x 2 + 67
We consider the new divisor 75 and the new remainder 67,and apply the division lemma to get
75 = 67 x 1 + 8
We consider the new divisor 67 and the new remainder 8,and apply the division lemma to get
67 = 8 x 8 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 726 and 509 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(67,8) = HCF(75,67) = HCF(217,75) = HCF(509,217) = HCF(726,509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 1, we apply the division lemma to 120 and 1, to get
120 = 1 x 120 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 120 is 1
Notice that 1 = HCF(120,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 648 > 1, we apply the division lemma to 648 and 1, to get
648 = 1 x 648 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 648 is 1
Notice that 1 = HCF(648,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 726, 509, 120, 648?
Answer: HCF of 726, 509, 120, 648 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 726, 509, 120, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 726, 509, 120, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.