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 204, 760, 737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 760, 737 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 204, 760, 737 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 204, 760, 737 is 1.
HCF(204, 760, 737) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 204, 760, 737 is 1.
Step 1: Since 760 > 204, we apply the division lemma to 760 and 204, to get
760 = 204 x 3 + 148
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 148 and 204, to get
204 = 148 x 1 + 56
Step 3: We consider the new divisor 148 and the new remainder 56, and apply the division lemma to get
148 = 56 x 2 + 36
We consider the new divisor 56 and the new remainder 36,and apply the division lemma to get
56 = 36 x 1 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 204 and 760 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(148,56) = HCF(204,148) = HCF(760,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 737 > 4, we apply the division lemma to 737 and 4, to get
737 = 4 x 184 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 737 is 1
Notice that 1 = HCF(4,1) = HCF(737,4) .
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 204, 760, 737?
Answer: HCF of 204, 760, 737 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 760, 737 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 760, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.