Highest Common Factor of 138, 186, 224, 61 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 138, 186, 224, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 186, 224, 61 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 138, 186, 224, 61 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 138, 186, 224, 61 is 1.
HCF(138, 186, 224, 61) = 1
HCF of 138, 186, 224, 61 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 186, 224, 61 is 1.
Highest Common Factor of 138,186,224,61 is 1
Step 1: Since 186 > 138, we apply the division lemma to 186 and 138, to get
186 = 138 x 1 + 48
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 48 and 138, to get
138 = 48 x 2 + 42
Step 3: We consider the new divisor 48 and the new remainder 42, and apply the division lemma to get
48 = 42 x 1 + 6
We consider the new divisor 42 and the new remainder 6, and apply the division lemma to get
42 = 6 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 138 and 186 is 6
Notice that 6 = HCF(42,6) = HCF(48,42) = HCF(138,48) = HCF(186,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 224 > 6, we apply the division lemma to 224 and 6, to get
224 = 6 x 37 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 224 is 2
Notice that 2 = HCF(6,2) = HCF(224,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61 > 2, we apply the division lemma to 61 and 2, to get
61 = 2 x 30 + 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 61 is 1
Notice that 1 = HCF(2,1) = HCF(61,2) .
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Frequently Asked Questions on HCF of 138, 186, 224, 61 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 138, 186, 224, 61?
Answer: HCF of 138, 186, 224, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 186, 224, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 186, 224, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.