Highest Common Factor of 138, 276, 907 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, 276, 907 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 276, 907 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, 276, 907 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, 276, 907 is 1.
HCF(138, 276, 907) = 1
HCF of 138, 276, 907 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, 276, 907 is 1.
Highest Common Factor of 138,276,907 is 1
Step 1: Since 276 > 138, we apply the division lemma to 276 and 138, to get
276 = 138 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 138, the HCF of 138 and 276 is 138
Notice that 138 = HCF(276,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 907 > 138, we apply the division lemma to 907 and 138, to get
907 = 138 x 6 + 79
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 79 and 138, to get
138 = 79 x 1 + 59
Step 3: We consider the new divisor 79 and the new remainder 59, and apply the division lemma to get
79 = 59 x 1 + 20
We consider the new divisor 59 and the new remainder 20,and apply the division lemma to get
59 = 20 x 2 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 138 and 907 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(59,20) = HCF(79,59) = HCF(138,79) = HCF(907,138) .
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Frequently Asked Questions on HCF of 138, 276, 907 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, 276, 907?
Answer: HCF of 138, 276, 907 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 276, 907 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 276, 907 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.