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 421, 494, 650 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 494, 650 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 421, 494, 650 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 421, 494, 650 is 1.
HCF(421, 494, 650) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 494, 650 is 1.
Step 1: Since 494 > 421, we apply the division lemma to 494 and 421, to get
494 = 421 x 1 + 73
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 73 and 421, to get
421 = 73 x 5 + 56
Step 3: We consider the new divisor 73 and the new remainder 56, and apply the division lemma to get
73 = 56 x 1 + 17
We consider the new divisor 56 and the new remainder 17,and apply the division lemma to get
56 = 17 x 3 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 421 and 494 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(56,17) = HCF(73,56) = HCF(421,73) = HCF(494,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 650 > 1, we apply the division lemma to 650 and 1, to get
650 = 1 x 650 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 650 is 1
Notice that 1 = HCF(650,1) .
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 421, 494, 650?
Answer: HCF of 421, 494, 650 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 494, 650 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 494, 650 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.