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 897, 460, 693 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 897, 460, 693 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 897, 460, 693 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 897, 460, 693 is 1.
HCF(897, 460, 693) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 897, 460, 693 is 1.
Step 1: Since 897 > 460, we apply the division lemma to 897 and 460, to get
897 = 460 x 1 + 437
Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 437 and 460, to get
460 = 437 x 1 + 23
Step 3: We consider the new divisor 437 and the new remainder 23, and apply the division lemma to get
437 = 23 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 897 and 460 is 23
Notice that 23 = HCF(437,23) = HCF(460,437) = HCF(897,460) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 693 > 23, we apply the division lemma to 693 and 23, to get
693 = 23 x 30 + 3
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 3 and 23, to get
23 = 3 x 7 + 2
Step 3: 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 23 and 693 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(693,23) .
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 897, 460, 693?
Answer: HCF of 897, 460, 693 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 897, 460, 693 using Euclid's Algorithm?
Answer: For arbitrary numbers 897, 460, 693 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.