Highest Common Factor of 118, 649, 154 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 118, 649, 154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 118, 649, 154 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 118, 649, 154 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 118, 649, 154 is 1.
HCF(118, 649, 154) = 1
HCF of 118, 649, 154 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 118, 649, 154 is 1.
Highest Common Factor of 118,649,154 is 1
Step 1: Since 649 > 118, we apply the division lemma to 649 and 118, to get
649 = 118 x 5 + 59
Step 2: Since the reminder 118 ≠ 0, we apply division lemma to 59 and 118, to get
118 = 59 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 118 and 649 is 59
Notice that 59 = HCF(118,59) = HCF(649,118) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 154 > 59, we apply the division lemma to 154 and 59, to get
154 = 59 x 2 + 36
Step 2: Since the reminder 59 ≠ 0, we apply division lemma to 36 and 59, to get
59 = 36 x 1 + 23
Step 3: We consider the new divisor 36 and the new remainder 23, and apply the division lemma to get
36 = 23 x 1 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 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 59 and 154 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(36,23) = HCF(59,36) = HCF(154,59) .
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Frequently Asked Questions on HCF of 118, 649, 154 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 118, 649, 154?
Answer: HCF of 118, 649, 154 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 118, 649, 154 using Euclid's Algorithm?
Answer: For arbitrary numbers 118, 649, 154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.