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 709, 874, 386, 39 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 709, 874, 386, 39 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 709, 874, 386, 39 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 709, 874, 386, 39 is 1.
HCF(709, 874, 386, 39) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 709, 874, 386, 39 is 1.
Step 1: Since 874 > 709, we apply the division lemma to 874 and 709, to get
874 = 709 x 1 + 165
Step 2: Since the reminder 709 ≠ 0, we apply division lemma to 165 and 709, to get
709 = 165 x 4 + 49
Step 3: We consider the new divisor 165 and the new remainder 49, and apply the division lemma to get
165 = 49 x 3 + 18
We consider the new divisor 49 and the new remainder 18,and apply the division lemma to get
49 = 18 x 2 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 709 and 874 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(49,18) = HCF(165,49) = HCF(709,165) = HCF(874,709) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 386 > 1, we apply the division lemma to 386 and 1, to get
386 = 1 x 386 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 386 is 1
Notice that 1 = HCF(386,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 39 > 1, we apply the division lemma to 39 and 1, to get
39 = 1 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 39 is 1
Notice that 1 = HCF(39,1) .
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 709, 874, 386, 39?
Answer: HCF of 709, 874, 386, 39 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 709, 874, 386, 39 using Euclid's Algorithm?
Answer: For arbitrary numbers 709, 874, 386, 39 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.