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 676, 160, 36, 317 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 160, 36, 317 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 676, 160, 36, 317 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 676, 160, 36, 317 is 1.
HCF(676, 160, 36, 317) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 676, 160, 36, 317 is 1.
Step 1: Since 676 > 160, we apply the division lemma to 676 and 160, to get
676 = 160 x 4 + 36
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 36 and 160, to get
160 = 36 x 4 + 16
Step 3: We consider the new divisor 36 and the new remainder 16, and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 676 and 160 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(160,36) = HCF(676,160) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 4, we apply the division lemma to 36 and 4, to get
36 = 4 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 36 is 4
Notice that 4 = HCF(36,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 317 > 4, we apply the division lemma to 317 and 4, to get
317 = 4 x 79 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 317 is 1
Notice that 1 = HCF(4,1) = HCF(317,4) .
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 676, 160, 36, 317?
Answer: HCF of 676, 160, 36, 317 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 160, 36, 317 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 160, 36, 317 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.