Highest Common Factor of 137, 648 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 137, 648 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 137, 648 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 137, 648 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 137, 648 is 1.
HCF(137, 648) = 1
HCF of 137, 648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 137, 648 is 1.
Highest Common Factor of 137,648 is 1
Step 1: Since 648 > 137, we apply the division lemma to 648 and 137, to get
648 = 137 x 4 + 100
Step 2: Since the reminder 137 ≠ 0, we apply division lemma to 100 and 137, to get
137 = 100 x 1 + 37
Step 3: We consider the new divisor 100 and the new remainder 37, and apply the division lemma to get
100 = 37 x 2 + 26
We consider the new divisor 37 and the new remainder 26,and apply the division lemma to get
37 = 26 x 1 + 11
We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get
26 = 11 x 2 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 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 137 and 648 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(100,37) = HCF(137,100) = HCF(648,137) .
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Frequently Asked Questions on HCF of 137, 648 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 137, 648?
Answer: HCF of 137, 648 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 137, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 137, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.