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 986, 746, 680, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 986, 746, 680, 27 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 986, 746, 680, 27 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 986, 746, 680, 27 is 1.
HCF(986, 746, 680, 27) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 986, 746, 680, 27 is 1.
Step 1: Since 986 > 746, we apply the division lemma to 986 and 746, to get
986 = 746 x 1 + 240
Step 2: Since the reminder 746 ≠ 0, we apply division lemma to 240 and 746, to get
746 = 240 x 3 + 26
Step 3: We consider the new divisor 240 and the new remainder 26, and apply the division lemma to get
240 = 26 x 9 + 6
We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get
26 = 6 x 4 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 986 and 746 is 2
Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(240,26) = HCF(746,240) = HCF(986,746) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 2, we apply the division lemma to 680 and 2, to get
680 = 2 x 340 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 680 is 2
Notice that 2 = HCF(680,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27 > 2, we apply the division lemma to 27 and 2, to get
27 = 2 x 13 + 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 27 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) .
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 986, 746, 680, 27?
Answer: HCF of 986, 746, 680, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 986, 746, 680, 27 using Euclid's Algorithm?
Answer: For arbitrary numbers 986, 746, 680, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.