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 656, 906, 96, 541 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 906, 96, 541 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 656, 906, 96, 541 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 656, 906, 96, 541 is 1.
HCF(656, 906, 96, 541) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 906, 96, 541 is 1.
Step 1: Since 906 > 656, we apply the division lemma to 906 and 656, to get
906 = 656 x 1 + 250
Step 2: Since the reminder 656 ≠ 0, we apply division lemma to 250 and 656, to get
656 = 250 x 2 + 156
Step 3: We consider the new divisor 250 and the new remainder 156, and apply the division lemma to get
250 = 156 x 1 + 94
We consider the new divisor 156 and the new remainder 94,and apply the division lemma to get
156 = 94 x 1 + 62
We consider the new divisor 94 and the new remainder 62,and apply the division lemma to get
94 = 62 x 1 + 32
We consider the new divisor 62 and the new remainder 32,and apply the division lemma to get
62 = 32 x 1 + 30
We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get
32 = 30 x 1 + 2
We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get
30 = 2 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 656 and 906 is 2
Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(62,32) = HCF(94,62) = HCF(156,94) = HCF(250,156) = HCF(656,250) = HCF(906,656) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 2, we apply the division lemma to 96 and 2, to get
96 = 2 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 96 is 2
Notice that 2 = HCF(96,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 541 > 2, we apply the division lemma to 541 and 2, to get
541 = 2 x 270 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 541 is 1
Notice that 1 = HCF(2,1) = HCF(541,2) .
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 656, 906, 96, 541?
Answer: HCF of 656, 906, 96, 541 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 906, 96, 541 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 906, 96, 541 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.