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 657, 946, 747 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 946, 747 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 657, 946, 747 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 657, 946, 747 is 1.
HCF(657, 946, 747) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 657, 946, 747 is 1.
Step 1: Since 946 > 657, we apply the division lemma to 946 and 657, to get
946 = 657 x 1 + 289
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 289 and 657, to get
657 = 289 x 2 + 79
Step 3: We consider the new divisor 289 and the new remainder 79, and apply the division lemma to get
289 = 79 x 3 + 52
We consider the new divisor 79 and the new remainder 52,and apply the division lemma to get
79 = 52 x 1 + 27
We consider the new divisor 52 and the new remainder 27,and apply the division lemma to get
52 = 27 x 1 + 25
We consider the new divisor 27 and the new remainder 25,and apply the division lemma to get
27 = 25 x 1 + 2
We consider the new divisor 25 and the new remainder 2,and apply the division lemma to get
25 = 2 x 12 + 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 657 and 946 is 1
Notice that 1 = HCF(2,1) = HCF(25,2) = HCF(27,25) = HCF(52,27) = HCF(79,52) = HCF(289,79) = HCF(657,289) = HCF(946,657) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 747 > 1, we apply the division lemma to 747 and 1, to get
747 = 1 x 747 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 747 is 1
Notice that 1 = HCF(747,1) .
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 657, 946, 747?
Answer: HCF of 657, 946, 747 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 946, 747 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 946, 747 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.