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 274, 691, 530 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 274, 691, 530 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 274, 691, 530 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 274, 691, 530 is 1.
HCF(274, 691, 530) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 274, 691, 530 is 1.
Step 1: Since 691 > 274, we apply the division lemma to 691 and 274, to get
691 = 274 x 2 + 143
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 143 and 274, to get
274 = 143 x 1 + 131
Step 3: We consider the new divisor 143 and the new remainder 131, and apply the division lemma to get
143 = 131 x 1 + 12
We consider the new divisor 131 and the new remainder 12,and apply the division lemma to get
131 = 12 x 10 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 274 and 691 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(131,12) = HCF(143,131) = HCF(274,143) = HCF(691,274) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 530 > 1, we apply the division lemma to 530 and 1, to get
530 = 1 x 530 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 530 is 1
Notice that 1 = HCF(530,1) .
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 274, 691, 530?
Answer: HCF of 274, 691, 530 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 274, 691, 530 using Euclid's Algorithm?
Answer: For arbitrary numbers 274, 691, 530 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.