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 789, 171, 688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 789, 171, 688 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 789, 171, 688 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 789, 171, 688 is 1.
HCF(789, 171, 688) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 789, 171, 688 is 1.
Step 1: Since 789 > 171, we apply the division lemma to 789 and 171, to get
789 = 171 x 4 + 105
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 105 and 171, to get
171 = 105 x 1 + 66
Step 3: We consider the new divisor 105 and the new remainder 66, and apply the division lemma to get
105 = 66 x 1 + 39
We consider the new divisor 66 and the new remainder 39,and apply the division lemma to get
66 = 39 x 1 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 789 and 171 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(66,39) = HCF(105,66) = HCF(171,105) = HCF(789,171) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 688 > 3, we apply the division lemma to 688 and 3, to get
688 = 3 x 229 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 688 is 1
Notice that 1 = HCF(3,1) = HCF(688,3) .
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 789, 171, 688?
Answer: HCF of 789, 171, 688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 789, 171, 688 using Euclid's Algorithm?
Answer: For arbitrary numbers 789, 171, 688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.