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 708, 767, 207 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 767, 207 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 708, 767, 207 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 708, 767, 207 is 1.
HCF(708, 767, 207) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 767, 207 is 1.
Step 1: Since 767 > 708, we apply the division lemma to 767 and 708, to get
767 = 708 x 1 + 59
Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 59 and 708, to get
708 = 59 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 708 and 767 is 59
Notice that 59 = HCF(708,59) = HCF(767,708) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 207 > 59, we apply the division lemma to 207 and 59, to get
207 = 59 x 3 + 30
Step 2: Since the reminder 59 ≠ 0, we apply division lemma to 30 and 59, to get
59 = 30 x 1 + 29
Step 3: We consider the new divisor 30 and the new remainder 29, and apply the division lemma to get
30 = 29 x 1 + 1
We consider the new divisor 29 and the new remainder 1, and apply the division lemma to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 59 and 207 is 1
Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(59,30) = HCF(207,59) .
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 708, 767, 207?
Answer: HCF of 708, 767, 207 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 767, 207 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 767, 207 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.