Highest Common Factor of 506, 308, 970 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 506, 308, 970 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 308, 970 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 506, 308, 970 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 506, 308, 970 is 2.
HCF(506, 308, 970) = 2
HCF of 506, 308, 970 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 506, 308, 970 is 2.
Highest Common Factor of 506,308,970 is 2
Step 1: Since 506 > 308, we apply the division lemma to 506 and 308, to get
506 = 308 x 1 + 198
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 198 and 308, to get
308 = 198 x 1 + 110
Step 3: We consider the new divisor 198 and the new remainder 110, and apply the division lemma to get
198 = 110 x 1 + 88
We consider the new divisor 110 and the new remainder 88,and apply the division lemma to get
110 = 88 x 1 + 22
We consider the new divisor 88 and the new remainder 22,and apply the division lemma to get
88 = 22 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 506 and 308 is 22
Notice that 22 = HCF(88,22) = HCF(110,88) = HCF(198,110) = HCF(308,198) = HCF(506,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 970 > 22, we apply the division lemma to 970 and 22, to get
970 = 22 x 44 + 2
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 2 and 22, to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 22 and 970 is 2
Notice that 2 = HCF(22,2) = HCF(970,22) .
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Frequently Asked Questions on HCF of 506, 308, 970 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 506, 308, 970?
Answer: HCF of 506, 308, 970 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 308, 970 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 308, 970 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.