Highest Common Factor of 874, 938, 346, 82 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 874, 938, 346, 82 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 938, 346, 82 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 874, 938, 346, 82 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 874, 938, 346, 82 is 2.
HCF(874, 938, 346, 82) = 2
HCF of 874, 938, 346, 82 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 938, 346, 82 is 2.
Highest Common Factor of 874,938,346,82 is 2
Step 1: Since 938 > 874, we apply the division lemma to 938 and 874, to get
938 = 874 x 1 + 64
Step 2: Since the reminder 874 ≠ 0, we apply division lemma to 64 and 874, to get
874 = 64 x 13 + 42
Step 3: We consider the new divisor 64 and the new remainder 42, and apply the division lemma to get
64 = 42 x 1 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 874 and 938 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(64,42) = HCF(874,64) = HCF(938,874) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 346 > 2, we apply the division lemma to 346 and 2, to get
346 = 2 x 173 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 346 is 2
Notice that 2 = HCF(346,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 2, we apply the division lemma to 82 and 2, to get
82 = 2 x 41 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 82 is 2
Notice that 2 = HCF(82,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 874, 938, 346, 82 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 874, 938, 346, 82?
Answer: HCF of 874, 938, 346, 82 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 938, 346, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 938, 346, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.