Highest Common Factor of 506, 370, 170 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, 370, 170 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 506, 370, 170 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, 370, 170 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, 370, 170 is 2.
HCF(506, 370, 170) = 2
HCF of 506, 370, 170 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, 370, 170 is 2.
Highest Common Factor of 506,370,170 is 2
Step 1: Since 506 > 370, we apply the division lemma to 506 and 370, to get
506 = 370 x 1 + 136
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 136 and 370, to get
370 = 136 x 2 + 98
Step 3: We consider the new divisor 136 and the new remainder 98, and apply the division lemma to get
136 = 98 x 1 + 38
We consider the new divisor 98 and the new remainder 38,and apply the division lemma to get
98 = 38 x 2 + 22
We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get
38 = 22 x 1 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 506 and 370 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(98,38) = HCF(136,98) = HCF(370,136) = HCF(506,370) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 170 > 2, we apply the division lemma to 170 and 2, to get
170 = 2 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 170 is 2
Notice that 2 = HCF(170,2) .
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Frequently Asked Questions on HCF of 506, 370, 170 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, 370, 170?
Answer: HCF of 506, 370, 170 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 506, 370, 170 using Euclid's Algorithm?
Answer: For arbitrary numbers 506, 370, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
