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 574, 709, 33, 609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 709, 33, 609 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 574, 709, 33, 609 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 574, 709, 33, 609 is 1.
HCF(574, 709, 33, 609) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 709, 33, 609 is 1.
Step 1: Since 709 > 574, we apply the division lemma to 709 and 574, to get
709 = 574 x 1 + 135
Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 135 and 574, to get
574 = 135 x 4 + 34
Step 3: We consider the new divisor 135 and the new remainder 34, and apply the division lemma to get
135 = 34 x 3 + 33
We consider the new divisor 34 and the new remainder 33,and apply the division lemma to get
34 = 33 x 1 + 1
We consider the new divisor 33 and the new remainder 1,and apply the division lemma to get
33 = 1 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 574 and 709 is 1
Notice that 1 = HCF(33,1) = HCF(34,33) = HCF(135,34) = HCF(574,135) = HCF(709,574) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 33 > 1, we apply the division lemma to 33 and 1, to get
33 = 1 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 33 is 1
Notice that 1 = HCF(33,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 609 > 1, we apply the division lemma to 609 and 1, to get
609 = 1 x 609 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 609 is 1
Notice that 1 = HCF(609,1) .
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 574, 709, 33, 609?
Answer: HCF of 574, 709, 33, 609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 709, 33, 609 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 709, 33, 609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.