Highest Common Factor of 140, 219, 900 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, 219, 900 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 140, 219, 900 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, 219, 900 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, 219, 900 is 1.
HCF(140, 219, 900) = 1
HCF of 140, 219, 900 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, 219, 900 is 1.
Highest Common Factor of 140,219,900 is 1
Step 1: Since 219 > 140, we apply the division lemma to 219 and 140, to get
219 = 140 x 1 + 79
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 79 and 140, to get
140 = 79 x 1 + 61
Step 3: We consider the new divisor 79 and the new remainder 61, and apply the division lemma to get
79 = 61 x 1 + 18
We consider the new divisor 61 and the new remainder 18,and apply the division lemma to get
61 = 18 x 3 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 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 140 and 219 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(61,18) = HCF(79,61) = HCF(140,79) = HCF(219,140) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 900 > 1, we apply the division lemma to 900 and 1, to get
900 = 1 x 900 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 900 is 1
Notice that 1 = HCF(900,1) .
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Frequently Asked Questions on HCF of 140, 219, 900 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, 219, 900?
Answer: HCF of 140, 219, 900 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 140, 219, 900 using Euclid's Algorithm?
Answer: For arbitrary numbers 140, 219, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.