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 616, 746, 705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 616, 746, 705 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 616, 746, 705 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 616, 746, 705 is 1.
HCF(616, 746, 705) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 616, 746, 705 is 1.
Step 1: Since 746 > 616, we apply the division lemma to 746 and 616, to get
746 = 616 x 1 + 130
Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 130 and 616, to get
616 = 130 x 4 + 96
Step 3: We consider the new divisor 130 and the new remainder 96, and apply the division lemma to get
130 = 96 x 1 + 34
We consider the new divisor 96 and the new remainder 34,and apply the division lemma to get
96 = 34 x 2 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 616 and 746 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(96,34) = HCF(130,96) = HCF(616,130) = HCF(746,616) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 705 > 2, we apply the division lemma to 705 and 2, to get
705 = 2 x 352 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 705 is 1
Notice that 1 = HCF(2,1) = HCF(705,2) .
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 616, 746, 705?
Answer: HCF of 616, 746, 705 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 616, 746, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 616, 746, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.