Highest Common Factor of 270, 972, 139 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 270, 972, 139 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 972, 139 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 270, 972, 139 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 270, 972, 139 is 1.
HCF(270, 972, 139) = 1
HCF of 270, 972, 139 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 972, 139 is 1.
Highest Common Factor of 270,972,139 is 1
Step 1: Since 972 > 270, we apply the division lemma to 972 and 270, to get
972 = 270 x 3 + 162
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 162 and 270, to get
270 = 162 x 1 + 108
Step 3: We consider the new divisor 162 and the new remainder 108, and apply the division lemma to get
162 = 108 x 1 + 54
We consider the new divisor 108 and the new remainder 54, and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 270 and 972 is 54
Notice that 54 = HCF(108,54) = HCF(162,108) = HCF(270,162) = HCF(972,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 139 > 54, we apply the division lemma to 139 and 54, to get
139 = 54 x 2 + 31
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 31 and 54, to get
54 = 31 x 1 + 23
Step 3: We consider the new divisor 31 and the new remainder 23, and apply the division lemma to get
31 = 23 x 1 + 8
We consider the new divisor 23 and the new remainder 8,and apply the division lemma to get
23 = 8 x 2 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 54 and 139 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(23,8) = HCF(31,23) = HCF(54,31) = HCF(139,54) .
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Frequently Asked Questions on HCF of 270, 972, 139 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 270, 972, 139?
Answer: HCF of 270, 972, 139 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 972, 139 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 972, 139 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.