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 921, 1588, 5658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 1588, 5658 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 921, 1588, 5658 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 921, 1588, 5658 is 1.
HCF(921, 1588, 5658) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 1588, 5658 is 1.
Step 1: Since 1588 > 921, we apply the division lemma to 1588 and 921, to get
1588 = 921 x 1 + 667
Step 2: Since the reminder 921 ≠ 0, we apply division lemma to 667 and 921, to get
921 = 667 x 1 + 254
Step 3: We consider the new divisor 667 and the new remainder 254, and apply the division lemma to get
667 = 254 x 2 + 159
We consider the new divisor 254 and the new remainder 159,and apply the division lemma to get
254 = 159 x 1 + 95
We consider the new divisor 159 and the new remainder 95,and apply the division lemma to get
159 = 95 x 1 + 64
We consider the new divisor 95 and the new remainder 64,and apply the division lemma to get
95 = 64 x 1 + 31
We consider the new divisor 64 and the new remainder 31,and apply the division lemma to get
64 = 31 x 2 + 2
We consider the new divisor 31 and the new remainder 2,and apply the division lemma to get
31 = 2 x 15 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 921 and 1588 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) = HCF(64,31) = HCF(95,64) = HCF(159,95) = HCF(254,159) = HCF(667,254) = HCF(921,667) = HCF(1588,921) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5658 > 1, we apply the division lemma to 5658 and 1, to get
5658 = 1 x 5658 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5658 is 1
Notice that 1 = HCF(5658,1) .
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 921, 1588, 5658?
Answer: HCF of 921, 1588, 5658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 1588, 5658 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 1588, 5658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.