Highest Common Factor of 148, 952, 70 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, 952, 70 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 148, 952, 70 is 2 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, 952, 70 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, 952, 70 is 2.
HCF(148, 952, 70) = 2
HCF of 148, 952, 70 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, 952, 70 is 2.
Highest Common Factor of 148,952,70 is 2
Step 1: Since 952 > 148, we apply the division lemma to 952 and 148, to get
952 = 148 x 6 + 64
Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 64 and 148, to get
148 = 64 x 2 + 20
Step 3: We consider the new divisor 64 and the new remainder 20, and apply the division lemma to get
64 = 20 x 3 + 4
We consider the new divisor 20 and the new remainder 4, and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 148 and 952 is 4
Notice that 4 = HCF(20,4) = HCF(64,20) = HCF(148,64) = HCF(952,148) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 4, we apply the division lemma to 70 and 4, to get
70 = 4 x 17 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 70 is 2
Notice that 2 = HCF(4,2) = HCF(70,4) .
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Frequently Asked Questions on HCF of 148, 952, 70 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, 952, 70?
Answer: HCF of 148, 952, 70 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 148, 952, 70 using Euclid's Algorithm?
Answer: For arbitrary numbers 148, 952, 70 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.