Highest Common Factor of 210, 121, 792, 78 using Euclid's algorithm
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 210, 121, 792, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 121, 792, 78 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 210, 121, 792, 78 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 210, 121, 792, 78 is 1.
HCF(210, 121, 792, 78) = 1
HCF of 210, 121, 792, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 121, 792, 78 is 1.
Highest Common Factor of 210,121,792,78 is 1
Step 1: Since 210 > 121, we apply the division lemma to 210 and 121, to get
210 = 121 x 1 + 89
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 89 and 121, to get
121 = 89 x 1 + 32
Step 3: We consider the new divisor 89 and the new remainder 32, and apply the division lemma to get
89 = 32 x 2 + 25
We consider the new divisor 32 and the new remainder 25,and apply the division lemma to get
32 = 25 x 1 + 7
We consider the new divisor 25 and the new remainder 7,and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 210 and 121 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(32,25) = HCF(89,32) = HCF(121,89) = HCF(210,121) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 792 > 1, we apply the division lemma to 792 and 1, to get
792 = 1 x 792 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 792 is 1
Notice that 1 = HCF(792,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
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Frequently Asked Questions on HCF of 210, 121, 792, 78 using Euclid's Algorithm
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 210, 121, 792, 78?
Answer: HCF of 210, 121, 792, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 121, 792, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 121, 792, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.