Highest Common Factor of 422, 974, 290 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 422, 974, 290 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 422, 974, 290 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 422, 974, 290 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 422, 974, 290 is 2.
HCF(422, 974, 290) = 2
HCF of 422, 974, 290 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 422, 974, 290 is 2.
Highest Common Factor of 422,974,290 is 2
Step 1: Since 974 > 422, we apply the division lemma to 974 and 422, to get
974 = 422 x 2 + 130
Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 130 and 422, to get
422 = 130 x 3 + 32
Step 3: We consider the new divisor 130 and the new remainder 32, and apply the division lemma to get
130 = 32 x 4 + 2
We consider the new divisor 32 and the new remainder 2, and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 974 is 2
Notice that 2 = HCF(32,2) = HCF(130,32) = HCF(422,130) = HCF(974,422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 290 > 2, we apply the division lemma to 290 and 2, to get
290 = 2 x 145 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 290 is 2
Notice that 2 = HCF(290,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 422, 974, 290 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 422, 974, 290?
Answer: HCF of 422, 974, 290 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 422, 974, 290 using Euclid's Algorithm?
Answer: For arbitrary numbers 422, 974, 290 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
