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 705, 740, 105, 607 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 740, 105, 607 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 705, 740, 105, 607 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 705, 740, 105, 607 is 1.
HCF(705, 740, 105, 607) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 740, 105, 607 is 1.
Step 1: Since 740 > 705, we apply the division lemma to 740 and 705, to get
740 = 705 x 1 + 35
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 35 and 705, to get
705 = 35 x 20 + 5
Step 3: We consider the new divisor 35 and the new remainder 5, and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 705 and 740 is 5
Notice that 5 = HCF(35,5) = HCF(705,35) = HCF(740,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 5, we apply the division lemma to 105 and 5, to get
105 = 5 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 105 is 5
Notice that 5 = HCF(105,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 607 > 5, we apply the division lemma to 607 and 5, to get
607 = 5 x 121 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 607 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(607,5) .
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 705, 740, 105, 607?
Answer: HCF of 705, 740, 105, 607 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 740, 105, 607 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 740, 105, 607 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.