Highest Common Factor of 148, 971, 167 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 148, 971, 167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 148, 971, 167 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 148, 971, 167 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 148, 971, 167 is 1.
HCF(148, 971, 167) = 1
HCF of 148, 971, 167 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 148, 971, 167 is 1.
Highest Common Factor of 148,971,167 is 1
Step 1: Since 971 > 148, we apply the division lemma to 971 and 148, to get
971 = 148 x 6 + 83
Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 83 and 148, to get
148 = 83 x 1 + 65
Step 3: We consider the new divisor 83 and the new remainder 65, and apply the division lemma to get
83 = 65 x 1 + 18
We consider the new divisor 65 and the new remainder 18,and apply the division lemma to get
65 = 18 x 3 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 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 148 and 971 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(65,18) = HCF(83,65) = HCF(148,83) = HCF(971,148) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 167 > 1, we apply the division lemma to 167 and 1, to get
167 = 1 x 167 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 167 is 1
Notice that 1 = HCF(167,1) .
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Frequently Asked Questions on HCF of 148, 971, 167 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 148, 971, 167?
Answer: HCF of 148, 971, 167 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 148, 971, 167 using Euclid's Algorithm?
Answer: For arbitrary numbers 148, 971, 167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.