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 985, 578, 949 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 578, 949 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 985, 578, 949 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 985, 578, 949 is 1.
HCF(985, 578, 949) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 578, 949 is 1.
Step 1: Since 985 > 578, we apply the division lemma to 985 and 578, to get
985 = 578 x 1 + 407
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 407 and 578, to get
578 = 407 x 1 + 171
Step 3: We consider the new divisor 407 and the new remainder 171, and apply the division lemma to get
407 = 171 x 2 + 65
We consider the new divisor 171 and the new remainder 65,and apply the division lemma to get
171 = 65 x 2 + 41
We consider the new divisor 65 and the new remainder 41,and apply the division lemma to get
65 = 41 x 1 + 24
We consider the new divisor 41 and the new remainder 24,and apply the division lemma to get
41 = 24 x 1 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 985 and 578 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(41,24) = HCF(65,41) = HCF(171,65) = HCF(407,171) = HCF(578,407) = HCF(985,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 949 > 1, we apply the division lemma to 949 and 1, to get
949 = 1 x 949 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 949 is 1
Notice that 1 = HCF(949,1) .
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 985, 578, 949?
Answer: HCF of 985, 578, 949 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 578, 949 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 578, 949 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.