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 597, 726, 758 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 597, 726, 758 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 597, 726, 758 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 597, 726, 758 is 1.
HCF(597, 726, 758) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 597, 726, 758 is 1.
Step 1: Since 726 > 597, we apply the division lemma to 726 and 597, to get
726 = 597 x 1 + 129
Step 2: Since the reminder 597 ≠ 0, we apply division lemma to 129 and 597, to get
597 = 129 x 4 + 81
Step 3: We consider the new divisor 129 and the new remainder 81, and apply the division lemma to get
129 = 81 x 1 + 48
We consider the new divisor 81 and the new remainder 48,and apply the division lemma to get
81 = 48 x 1 + 33
We consider the new divisor 48 and the new remainder 33,and apply the division lemma to get
48 = 33 x 1 + 15
We consider the new divisor 33 and the new remainder 15,and apply the division lemma to get
33 = 15 x 2 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 597 and 726 is 3
Notice that 3 = HCF(15,3) = HCF(33,15) = HCF(48,33) = HCF(81,48) = HCF(129,81) = HCF(597,129) = HCF(726,597) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 758 > 3, we apply the division lemma to 758 and 3, to get
758 = 3 x 252 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 758 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(758,3) .
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 597, 726, 758?
Answer: HCF of 597, 726, 758 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 597, 726, 758 using Euclid's Algorithm?
Answer: For arbitrary numbers 597, 726, 758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.