Highest Common Factor of 140, 918, 872, 213 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 140, 918, 872, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 140, 918, 872, 213 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 140, 918, 872, 213 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 140, 918, 872, 213 is 1.
HCF(140, 918, 872, 213) = 1
HCF of 140, 918, 872, 213 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 140, 918, 872, 213 is 1.
Highest Common Factor of 140,918,872,213 is 1
Step 1: Since 918 > 140, we apply the division lemma to 918 and 140, to get
918 = 140 x 6 + 78
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 78 and 140, to get
140 = 78 x 1 + 62
Step 3: We consider the new divisor 78 and the new remainder 62, and apply the division lemma to get
78 = 62 x 1 + 16
We consider the new divisor 62 and the new remainder 16,and apply the division lemma to get
62 = 16 x 3 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 140 and 918 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(62,16) = HCF(78,62) = HCF(140,78) = HCF(918,140) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 872 > 2, we apply the division lemma to 872 and 2, to get
872 = 2 x 436 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 872 is 2
Notice that 2 = HCF(872,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 213 > 2, we apply the division lemma to 213 and 2, to get
213 = 2 x 106 + 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 213 is 1
Notice that 1 = HCF(2,1) = HCF(213,2) .
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Frequently Asked Questions on HCF of 140, 918, 872, 213 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 140, 918, 872, 213?
Answer: HCF of 140, 918, 872, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 140, 918, 872, 213 using Euclid's Algorithm?
Answer: For arbitrary numbers 140, 918, 872, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.