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 857, 503, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 503, 78 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 857, 503, 78 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 857, 503, 78 is 1.
HCF(857, 503, 78) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 503, 78 is 1.
Step 1: Since 857 > 503, we apply the division lemma to 857 and 503, to get
857 = 503 x 1 + 354
Step 2: Since the reminder 503 ≠ 0, we apply division lemma to 354 and 503, to get
503 = 354 x 1 + 149
Step 3: We consider the new divisor 354 and the new remainder 149, and apply the division lemma to get
354 = 149 x 2 + 56
We consider the new divisor 149 and the new remainder 56,and apply the division lemma to get
149 = 56 x 2 + 37
We consider the new divisor 56 and the new remainder 37,and apply the division lemma to get
56 = 37 x 1 + 19
We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get
37 = 19 x 1 + 18
We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get
19 = 18 x 1 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 503 is 1
Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(149,56) = HCF(354,149) = HCF(503,354) = HCF(857,503) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
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 857, 503, 78?
Answer: HCF of 857, 503, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 503, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 503, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.