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 617, 456, 685 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 617, 456, 685 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 617, 456, 685 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 617, 456, 685 is 1.
HCF(617, 456, 685) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 617, 456, 685 is 1.
Step 1: Since 617 > 456, we apply the division lemma to 617 and 456, to get
617 = 456 x 1 + 161
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 161 and 456, to get
456 = 161 x 2 + 134
Step 3: We consider the new divisor 161 and the new remainder 134, and apply the division lemma to get
161 = 134 x 1 + 27
We consider the new divisor 134 and the new remainder 27,and apply the division lemma to get
134 = 27 x 4 + 26
We consider the new divisor 27 and the new remainder 26,and apply the division lemma to get
27 = 26 x 1 + 1
We consider the new divisor 26 and the new remainder 1,and apply the division lemma to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 617 and 456 is 1
Notice that 1 = HCF(26,1) = HCF(27,26) = HCF(134,27) = HCF(161,134) = HCF(456,161) = HCF(617,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 685 > 1, we apply the division lemma to 685 and 1, to get
685 = 1 x 685 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 685 is 1
Notice that 1 = HCF(685,1) .
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 617, 456, 685?
Answer: HCF of 617, 456, 685 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 617, 456, 685 using Euclid's Algorithm?
Answer: For arbitrary numbers 617, 456, 685 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.