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, 1122, 5646 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 726, 1122, 5646 is 6 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, 1122, 5646 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, 1122, 5646 is 6.
HCF(726, 1122, 5646) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 726, 1122, 5646 is 6.
Step 1: Since 1122 > 726, we apply the division lemma to 1122 and 726, to get
1122 = 726 x 1 + 396
Step 2: Since the reminder 726 ≠ 0, we apply division lemma to 396 and 726, to get
726 = 396 x 1 + 330
Step 3: We consider the new divisor 396 and the new remainder 330, and apply the division lemma to get
396 = 330 x 1 + 66
We consider the new divisor 330 and the new remainder 66, and apply the division lemma to get
330 = 66 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 66, the HCF of 726 and 1122 is 66
Notice that 66 = HCF(330,66) = HCF(396,330) = HCF(726,396) = HCF(1122,726) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5646 > 66, we apply the division lemma to 5646 and 66, to get
5646 = 66 x 85 + 36
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 36 and 66, to get
66 = 36 x 1 + 30
Step 3: We consider the new divisor 36 and the new remainder 30, and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 66 and 5646 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(66,36) = HCF(5646,66) .
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, 1122, 5646?
Answer: HCF of 726, 1122, 5646 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 726, 1122, 5646 using Euclid's Algorithm?
Answer: For arbitrary numbers 726, 1122, 5646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.