Highest Common Factor of 42, 66, 70, 138 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 42, 66, 70, 138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 42, 66, 70, 138 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 42, 66, 70, 138 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 42, 66, 70, 138 is 2.
HCF(42, 66, 70, 138) = 2
HCF of 42, 66, 70, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 42, 66, 70, 138 is 2.
Highest Common Factor of 42,66,70,138 is 2
Step 1: Since 66 > 42, we apply the division lemma to 66 and 42, to get
66 = 42 x 1 + 24
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 24 and 42, to get
42 = 24 x 1 + 18
Step 3: We consider the new divisor 24 and the new remainder 18, and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 42 and 66 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(66,42) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70 > 6, we apply the division lemma to 70 and 6, to get
70 = 6 x 11 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma 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 6 and 70 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(70,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 138 > 2, we apply the division lemma to 138 and 2, to get
138 = 2 x 69 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 138 is 2
Notice that 2 = HCF(138,2) .
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Frequently Asked Questions on HCF of 42, 66, 70, 138 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 42, 66, 70, 138?
Answer: HCF of 42, 66, 70, 138 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 42, 66, 70, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 42, 66, 70, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.