Highest Common Factor of 646, 428, 690, 464 using Euclid's algorithm
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 646, 428, 690, 464 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 646, 428, 690, 464 is 2 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 646, 428, 690, 464 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 646, 428, 690, 464 is 2.
HCF(646, 428, 690, 464) = 2
HCF of 646, 428, 690, 464 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 646, 428, 690, 464 is 2.
Highest Common Factor of 646,428,690,464 is 2
Step 1: Since 646 > 428, we apply the division lemma to 646 and 428, to get
646 = 428 x 1 + 218
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 218 and 428, to get
428 = 218 x 1 + 210
Step 3: We consider the new divisor 218 and the new remainder 210, and apply the division lemma to get
218 = 210 x 1 + 8
We consider the new divisor 210 and the new remainder 8,and apply the division lemma to get
210 = 8 x 26 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 646 and 428 is 2
Notice that 2 = HCF(8,2) = HCF(210,8) = HCF(218,210) = HCF(428,218) = HCF(646,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 690 > 2, we apply the division lemma to 690 and 2, to get
690 = 2 x 345 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 690 is 2
Notice that 2 = HCF(690,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 464 > 2, we apply the division lemma to 464 and 2, to get
464 = 2 x 232 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 464 is 2
Notice that 2 = HCF(464,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 646, 428, 690, 464 using Euclid's Algorithm
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 646, 428, 690, 464?
Answer: HCF of 646, 428, 690, 464 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 646, 428, 690, 464 using Euclid's Algorithm?
Answer: For arbitrary numbers 646, 428, 690, 464 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.