Highest Common Factor of 137, 105, 606, 21 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, 105, 606, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 137, 105, 606, 21 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, 105, 606, 21 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, 105, 606, 21 is 1.
HCF(137, 105, 606, 21) = 1
HCF of 137, 105, 606, 21 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, 105, 606, 21 is 1.
Highest Common Factor of 137,105,606,21 is 1
Step 1: Since 137 > 105, we apply the division lemma to 137 and 105, to get
137 = 105 x 1 + 32
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 32 and 105, to get
105 = 32 x 3 + 9
Step 3: We consider the new divisor 32 and the new remainder 9, and apply the division lemma to get
32 = 9 x 3 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 137 and 105 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(105,32) = HCF(137,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 606 > 1, we apply the division lemma to 606 and 1, to get
606 = 1 x 606 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 606 is 1
Notice that 1 = HCF(606,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
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Frequently Asked Questions on HCF of 137, 105, 606, 21 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, 105, 606, 21?
Answer: HCF of 137, 105, 606, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 137, 105, 606, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 137, 105, 606, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.