Highest Common Factor of 874, 754, 854 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, 754, 854 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 754, 854 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, 754, 854 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, 754, 854 is 2.
HCF(874, 754, 854) = 2
HCF of 874, 754, 854 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, 754, 854 is 2.
Highest Common Factor of 874,754,854 is 2
Step 1: Since 874 > 754, we apply the division lemma to 874 and 754, to get
874 = 754 x 1 + 120
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 120 and 754, to get
754 = 120 x 6 + 34
Step 3: We consider the new divisor 120 and the new remainder 34, and apply the division lemma to get
120 = 34 x 3 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 874 and 754 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(120,34) = HCF(754,120) = HCF(874,754) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 854 > 2, we apply the division lemma to 854 and 2, to get
854 = 2 x 427 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 854 is 2
Notice that 2 = HCF(854,2) .
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, 754, 854 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, 754, 854?
Answer: HCF of 874, 754, 854 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 754, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 754, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.