Highest Common Factor of 494, 874, 376 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 494, 874, 376 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 494, 874, 376 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 494, 874, 376 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 494, 874, 376 is 2.
HCF(494, 874, 376) = 2
HCF of 494, 874, 376 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 494, 874, 376 is 2.
Highest Common Factor of 494,874,376 is 2
Step 1: Since 874 > 494, we apply the division lemma to 874 and 494, to get
874 = 494 x 1 + 380
Step 2: Since the reminder 494 ≠ 0, we apply division lemma to 380 and 494, to get
494 = 380 x 1 + 114
Step 3: We consider the new divisor 380 and the new remainder 114, and apply the division lemma to get
380 = 114 x 3 + 38
We consider the new divisor 114 and the new remainder 38, and apply the division lemma to get
114 = 38 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 494 and 874 is 38
Notice that 38 = HCF(114,38) = HCF(380,114) = HCF(494,380) = HCF(874,494) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 376 > 38, we apply the division lemma to 376 and 38, to get
376 = 38 x 9 + 34
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 34 and 38, to get
38 = 34 x 1 + 4
Step 3: We consider the new divisor 34 and the new remainder 4, and apply the division lemma to get
34 = 4 x 8 + 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 38 and 376 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(38,34) = HCF(376,38) .
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Frequently Asked Questions on HCF of 494, 874, 376 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 494, 874, 376?
Answer: HCF of 494, 874, 376 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 494, 874, 376 using Euclid's Algorithm?
Answer: For arbitrary numbers 494, 874, 376 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.