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 781, 678, 851, 910 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 781, 678, 851, 910 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 781, 678, 851, 910 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 781, 678, 851, 910 is 1.
HCF(781, 678, 851, 910) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 781, 678, 851, 910 is 1.
Step 1: Since 781 > 678, we apply the division lemma to 781 and 678, to get
781 = 678 x 1 + 103
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 103 and 678, to get
678 = 103 x 6 + 60
Step 3: We consider the new divisor 103 and the new remainder 60, and apply the division lemma to get
103 = 60 x 1 + 43
We consider the new divisor 60 and the new remainder 43,and apply the division lemma to get
60 = 43 x 1 + 17
We consider the new divisor 43 and the new remainder 17,and apply the division lemma to get
43 = 17 x 2 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 781 and 678 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(43,17) = HCF(60,43) = HCF(103,60) = HCF(678,103) = HCF(781,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 851 > 1, we apply the division lemma to 851 and 1, to get
851 = 1 x 851 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 851 is 1
Notice that 1 = HCF(851,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 910 > 1, we apply the division lemma to 910 and 1, to get
910 = 1 x 910 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 910 is 1
Notice that 1 = HCF(910,1) .
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 781, 678, 851, 910?
Answer: HCF of 781, 678, 851, 910 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 781, 678, 851, 910 using Euclid's Algorithm?
Answer: For arbitrary numbers 781, 678, 851, 910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.