Highest Common Factor of 70, 98, 42, 126 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 70, 98, 42, 126 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 98, 42, 126 is 14 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 70, 98, 42, 126 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 70, 98, 42, 126 is 14.
HCF(70, 98, 42, 126) = 14
HCF of 70, 98, 42, 126 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 98, 42, 126 is 14.
Highest Common Factor of 70,98,42,126 is 14
Step 1: Since 98 > 70, we apply the division lemma to 98 and 70, to get
98 = 70 x 1 + 28
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 28 and 70, to get
70 = 28 x 2 + 14
Step 3: We consider the new divisor 28 and the new remainder 14, and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 70 and 98 is 14
Notice that 14 = HCF(28,14) = HCF(70,28) = HCF(98,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 14, we apply the division lemma to 42 and 14, to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 42 is 14
Notice that 14 = HCF(42,14) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 126 > 14, we apply the division lemma to 126 and 14, to get
126 = 14 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 14 and 126 is 14
Notice that 14 = HCF(126,14) .
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Frequently Asked Questions on HCF of 70, 98, 42, 126 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 70, 98, 42, 126?
Answer: HCF of 70, 98, 42, 126 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 98, 42, 126 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 98, 42, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.