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, 545, 370 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 545, 370 is 1 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, 545, 370 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, 545, 370 is 1.
HCF(874, 545, 370) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 545, 370 is 1.
Step 1: Since 874 > 545, we apply the division lemma to 874 and 545, to get
874 = 545 x 1 + 329
Step 2: Since the reminder 545 ≠ 0, we apply division lemma to 329 and 545, to get
545 = 329 x 1 + 216
Step 3: We consider the new divisor 329 and the new remainder 216, and apply the division lemma to get
329 = 216 x 1 + 113
We consider the new divisor 216 and the new remainder 113,and apply the division lemma to get
216 = 113 x 1 + 103
We consider the new divisor 113 and the new remainder 103,and apply the division lemma to get
113 = 103 x 1 + 10
We consider the new divisor 103 and the new remainder 10,and apply the division lemma to get
103 = 10 x 10 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 874 and 545 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(103,10) = HCF(113,103) = HCF(216,113) = HCF(329,216) = HCF(545,329) = HCF(874,545) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 1, we apply the division lemma to 370 and 1, to get
370 = 1 x 370 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 370 is 1
Notice that 1 = HCF(370,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 545, 370?
Answer: HCF of 874, 545, 370 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 545, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 545, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.